Math Fundamentals for
Statistics II (Math 95)
Homework Unit 1:
Finance
Scott Fallstrom and Brent Pickett
“The ‘How’ and ‘Whys’ Guys”
This work is licensed under a Creative Commons AttributionNonCommercial-ShareAlike 4.0 International License
2nd Edition (Summer 2016)
Math 95 – Homework Unit 1 – Page 1
1.1: Starting Simple
Vocabulary and symbols – write out what the following mean:




Principal, P
Term, t
Interest Rate, r
Simple Interest, I




I  P r t
Future Value
Present Value
FV  P 1  r  t 


Add-on Interest
Average Daily Balance
(ADB)
Concept questions:
1. Why is the present value the same as the principal?
2. When dealing with simple interest, why does the amount of time on the interest rate and the term have
to match?
3. Rebekah is computing simple interest based on a principal of $400 with 5% annual simple interest for 8
months and she does I  40058  16,000 . Explain her mistakes.
4. Leah is computing simple interest based on a principal of $400 with 5% annual simple interest for 8
months and she does I  4000.058  160 . Explain her mistakes.
5. Joshua is computing simple interest based on a principal of $400 with 5% annual simple interest for 8
8
months and she does I  4005   16,000 . Explain his mistakes.
 12 
6. What type of sequence is simple interest similar to: arithmetic or geometric? Explain why.
7. Simple interest earns interest on the principal and any interest in the account. True or false? Explain.
8. In the finance formulas, what does it mean to be in capital letters and why is this important?
Exercises:
9. Find the amount of simple interest from the following:
a. A loan of $1,200 at 4.25% annual simple interest for 5 years.
b. A loan of $15,200 at 7.25% annual simple interest for 15 years.
c. A loan of $15,200 at 7.25% annual simple interest for 15 months.
d. An investment of $5,900 at 2.25% monthly simple interest for 15 years.
e. An investment of $5,900 at 2.25% monthly simple interest for 15 months.
f. An investment of $5,900 at 2.25% annual simple interest for 15 years.
g. An investment of $5,900 at 2.25% annual simple interest for 15 days.
h. The interest on a payday loan of $50 at 460.42% annual simple interest for 14 days.
i. The interest on a payday loan of $50 at 460.42% annual simple interest for 1 month.
j. The interest on a payday loan of $50 at 460.42% annual simple interest for 1 year.
k. The interest on an investment of $50,000 at 46.42% monthly simple interest for 6 months.
Math 95 – Homework Unit 1 – Page 2
10. Solve these simple interest problems for the missing piece (all are from California).
a. MoneyTree® offers a loan that charges $45 on a loan of $255 for 14 days. What is the annual simple
interest rate?
b. MoneyTree® offers a loan that charges $45 on a loan of $255 for 14 days. What is the daily simple
interest rate?
c. MoneyTree® offers a loan that charges $26.47 on a loan of $150 for 14 days. What is the annual
simple interest rate?
11. Solve these simple interest problems for the missing piece (all are from Washington state).
a. MoneyTree® offers a loan that charges $37.50 on a loan of $250 for 14 days. What is the annual
simple interest rate?
b. MoneyTree® offers a loan that charges $60 on a loan of $400 for 14 days. What is the annual simple
interest rate?
c. MoneyTree® offers a loan that charges $95 on a loan of $700 for 14 days. What is the annual simple
interest rate?
12. Solve these simple interest problems for the missing piece.
a. Find the annual simple interest rate for a loan of 45 days requiring $50 interest on principal of $650.
b. Find the annual simple interest rate for a loan of 4 years requiring $700 interest on principal of
$6,500.
c. Find the annual simple interest rate for a loan of 60 months with $2,350 interest on principal of
$32,000.
d. Find the monthly simple interest rate for a loan of 60 months with $2,350 interest on principal of
$32,000.
e. Find the principal needed to earn $75 in interest on 6% annual simple interest over 3 years.
f. Find the principal needed to earn $27 in interest on 5% monthly simple interest over 3 months.
g. Find the principal needed to earn $79 in interest on 5% annual simple interest over 3 months.
h. Find the principal needed to earn $370 in interest on 4.3% annual simple interest over 45 days.
i. Find the time needed to earn $50 in interest on an investment of $500 at 5% annual simple interest.
j. Find the time needed to earn $700 in interest on an investment of $500 at 4% annual simple interest.
k. Find the time needed to earn $700 in interest on an investment of $500 at 4% monthly simple
interest.
13. What is the future value of …
a. $950 at 3% annual simple interest for 13 months?
b. $950 at 4.75% annual simple interest for 13 months?
c. $950 at 4.75% monthly simple interest for 13 months?
d. $1,950 at 11.25% annual simple interest for 13 days?
e. $1,950 at 11.25% annual simple interest for 13 years?
14. Determine the present value that will yield a future value of…
a. $3,500 at 5% annual simple interest for 2 years.
b. $2,400 at 13% annual simple interest for 2 months.
c. $2,400 at 13% monthly simple interest for 2 months.
d. $2,400 at 13% annual simple interest for 2 days.
e. $29,400 at 8% annual simple interest for 2 years.
f. $59,400 at 18% annual simple interest for 20 years.
Math 95 – Homework Unit 1 – Page 3
15. Determine the monthly payment and total interest paid for the following add-on interest loans.
a. The principal amount is $850 at 9% annual simple interest for 2 years.
b. The principal amount is $58,000 at 3.75% annual simple interest for 7 years.
c. The principal amount is $58,000 at 3.75% annual simple interest for 2 years.
d. Explain the reason for choosing the 7 year loan (above) instead of the 2 year loan (above).
e. Explain the reason for choosing the 2 year loan (above) instead of the 7 year loan (above).
To help, it is good to remember the following about our calendar and the number of days in each.
January – 31
May – 31
September – 30
February – 28 (or 29)
June – 30
October – 31
March – 31
July – 31
November – 30
April – 30
August – 31
December – 31
Rule of Thumb – Credit Card Finance Charge: A rule of thumb for determining the finance charge is to
take the interest rate and divide by 12, then round to the nearest half (0.5, 1, 1.5, etc). Move the decimal
place on the principal two to the left, then multiply the two. Example: $3,000 at 14% annual simple
interest over June. Work: 14  12  1 and 3,000  30 . Multiply 1 × 30 = 30. So the finance charge will be
about $30.
16. Use the rule of thumb to estimate the finance charge for the following:
a. $1,000 at 18% annual simple interest over July.
b. $5,000 at 13% annual simple interest over April.
c. $25,000 at 11% annual simple interest over August.
d. $40,000 at 5% annual simple interest over January.
17. Determine the finance charge for the credit card based on the following information:
a. ADB is $1,100 at 19.99% annual simple interest over June.
b. ADB is $15,762 (average American credit card debt) at 14.9% annual simple interest (average
American credit card rate) over September.
c. ADB is $152 at 17.99% annual simple interest over January. First – ballpark this and decide if you
think the finance charge will be less than $5, between $5 and $15, or more than $15?
18. Determine (i) the finance charge, (ii) the new balance, and (iii) the minimum payment amount. Assume
the credit card requires 3% rounded up to nearest $5.
a. Peter has a credit card with an ADB of $3,694.78, with a remaining balance of $3,753.91. His
interest rate is 16.99% simple interest over December.
b. Ophelia has a credit card with an ADB of $984.28, with a remaining balance of $890.25. Her
interest rate is 22.99% simple interest over March.
c. The average American. ADB is $15,762 (average American credit card debt) at 14.9% annual
simple interest (average American credit card rate) over April, with remaining balance of $16,100.
d. The average American. ADB is $15,762 (average American credit card debt) at 14.9% annual
simple interest (average American credit card rate) over May, with remaining balance of $16,100.
e. The average American. ADB is $15,762 (average American credit card debt) at 23.9% annual
simple interest over May, with remaining balance of $16,100.
Wrap-up and look back:
19. What is the difference between present value and future value?
Math 95 – Homework Unit 1 – Page 4
20. What is the difference between I  P  r  t and FV  P1  r  t  ? When would you use each?
21. In order to get $5,000 in 3 months, do we need to invest more than $5,000, less than $5,000, or exactly
$5,000? At least 1 is correct. Explain.
22. Write in words what you learned from this section. Did you have any questions remaining that weren’t
covered in class? Write them out and bring them back to class.
1.2: Compounding Problems
Vocabulary and symbols – write out what the following mean:


Periodic Rate , i
nt
FV  P1  nr 


FV  P1  i 
Future Value Interest Factor (FVIF Table)
nt
Concept questions:
1. What is the difference between the interest rate, r, and the periodic rate, i?
2. If the interest rate is 6% annual interest, will the periodic rate be higher or lower than this? Explain.
3. If the interest rate is 6% annual interest, which periodic rate is higher: quarterly or monthly? Explain.
4. If the interest rate is 6% annual interest, which periodic rate is higher: bi-weekly or semi-monthly?
Explain.
5. If the interest rate is 6% annual interest, which periodic rate is higher: semi-annually or quarterly?
Explain.
6. Why is the future value of simple interest nearly the same as compound interest when the amount of
time is short?
7. Why is the future value of simple interest so much less than compound interest when the amount of
time is long?
8. If the present value is less than the future value, is the investment making money or losing it? Why?
Exercises:
This table may be helpful during the homework and these are the most common periods:
Time Measurement # of Compounding Periods
Time Measurement # of Compounding Periods
Annually
1
Semi-Annually
2
Quarterly
4
Monthly
12
Semi-Monthly
24
Bi-weekly
26
Weekly
52
Daily
365
Math 95 – Homework Unit 1 – Page 5
9. Find the periodic rate for these rate and compound time values.
d. 4.25% annual interest, quarterly.
a. 36% annual interest, quarterly.
b. 36% annual interest, annually.
e. 18% annual interest, monthly.
c. 36% annual interest, semi-annually.
f. 18% annual interest, daily.
10. Find the future value of $20,000 at 6% annual interest compounded monthly after: (a) 3 months, (b) 1
year, (c) 10 years, (d) 30 years. Compare each with the value using 6% annual simple interest. Round to
the nearest penny at the end of the computations.
11. Explore with compound interest:
a. Determine the future value of $9,000 at 2.99% annual interest compounded weekly for 10 years,
and determine the amount of interest earned.
b. Determine the future value of $4,500 at 7.49% annual interest compounded monthly for 13 months,
and determine the amount of interest earned.
c. Determine the future value of $4,500 at 7.49% annual interest compounded monthly for 15 years,
and determine the amount of interest earned.
d. Determine the present value of $19,000 at 5% annual interest compounded daily for 7 years, and
determine the amount of interest earned.
e. Determine the present value of $19,000 at 5% annual interest compounded monthly for 7 months,
and determine the amount of interest earned.
f. Determine the present value of $650,000 at 5.6% annual interest compounded monthly for 27 years,
and determine the amount of interest earned.
12. Try out a few more problems using inflation.
a. The long term average inflation rate for health care prices is 5.42% annually. If a health care plan
costs $912 per month now…
i. What is the annual health care cost now?
ii. What is the annual health care cost 20 years from now?
iii. What would be the monthly health care cost 20 years from now?
b. If wages and salaries are rising at about 1.5% annually. If a job has a salary of $59,000 per year
now, how much would that salary be 15 years from now?
c. Assuming that inflation is 2.2% annually, and you currently pay $3.19 for gas…
i.
How much will you pay for gas 20 years from now?
ii.
How much would you have paid for gas 10 years ago? (Hint – use a negative exponent!)
d. Tuition has been rising at about 7% annually for the past 30 years. If this continues, how much
would the tuition be at UCSD in 20 years ($26,738 per year in 2016)?
Math 95 – Homework Unit 1 – Page 6
TABLE 1 (Part 1 of 2)
(FVIF – Future Value Interest Factor for 1% to 7%)
Periods
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 1%
1.0100 1.0201 1.0303 1.0406 1.0510 1.0615 1.0721 1.0829 1.0937 1.1046 1.1157 1.1268 1.1381 1.1495 1.1610 1.1726 1.1843 1.1961 1.2081 1.2202 1.2324 1.2447 1.2572 1.2697 1.2824 1.2953 1.3082 1.3213 1.3345 1.3478 1.3613 1.3749 1.3887 1.4026 1.4166 1.4308 1.4451 1.4595 1.4741 1.4889 2%
1.0200 1.0404 1.0612 1.0824 1.1041 1.1262 1.1487 1.1717 1.1951 1.2190 1.2434 1.2682 1.2936 1.3195 1.3459 1.3728 1.4002 1.4282 1.4568 1.4859 1.5157 1.5460 1.5769 1.6084 1.6406 1.6734 1.7069 1.7410 1.7758 1.8114 1.8476 1.8845 1.9222 1.9607 1.9999 2.0399 2.0807 2.1223 2.1647 2.2080 3%
1.0300 1.0609 1.0927 1.1255 1.1593 1.1941 1.2299 1.2668 1.3048 1.3439 1.3842 1.4258 1.4685 1.5126 1.5580 1.6047 1.6528 1.7024 1.7535 1.8061 1.8603 1.9161 1.9736 2.0328 2.0938 2.1566 2.2213 2.2879 2.3566 2.4273 2.5001 2.5751 2.6523 2.7319 2.8139 2.8983 2.9852 3.0748 3.1670 3.2620 4%
1.0400 1.0816 1.1249 1.1699 1.2167 1.2653 1.3159 1.3686 1.4233 1.4802 1.5395 1.6010 1.6651 1.7317 1.8009 1.8730 1.9479 2.0258 2.1068 2.1911 2.2788 2.3699 2.4647 2.5633 2.6658 2.7725 2.8834 2.9987 3.1187 3.2434 3.3731 3.5081 3.6484 3.7943 3.9461 4.1039 4.2681 4.4388 4.6164 4.8010 5%
1.0500 1.1025 1.1576 1.2155 1.2763 1.3401 1.4071 1.4775 1.5513 1.6289 1.7103 1.7959 1.8856 1.9799 2.0789 2.1829 2.2920 2.4066 2.5270 2.6533 2.7860 2.9253 3.0715 3.2251 3.3864 3.5557 3.7335 3.9201 4.1161 4.3219 4.5380 4.7649 5.0032 5.2533 5.5160 5.7918 6.0814 6.3855 6.7048 7.0400 6%
1.0600 1.1236 1.1910 1.2625 1.3382 1.4185 1.5036 1.5938 1.6895 1.7908 1.8983 2.0122 2.1329 2.2609 2.3966 2.5404 2.6928 2.8543 3.0256 3.2071 3.3996 3.6035 3.8197 4.0489 4.2919 4.5494 4.8223 5.1117 5.4184 5.7435 6.0881 6.4534 6.8406 7.2510 7.6861 8.1473 8.6361 9.1543 9.7035 10.2857 7%
1.0700 1.1449 1.2250 1.3108 1.4026 1.5007 1.6058 1.7182 1.8385 1.9672 2.1049 2.2522 2.4098 2.5785 2.7590 2.9522 3.1588 3.3799 3.6165 3.8697 4.1406 4.4304 4.7405 5.0724 5.4274 5.8074 6.2139 6.6488 7.1143 7.6123 8.1451 8.7153 9.3253 9.9781 10.6766 11.4239 12.2236 13.0793 13.9948 14.9745 Math 95 – Homework Unit 1 – Page 7
TABLE 1 (Part 2 of 2)
(FVIF – Future Value Interest Factor for 8% to 14%)
Periods
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 8%
1.0800 1.1664 1.2597 1.3605 1.4693 1.5869 1.7138 1.8509 1.9990 2.1589 2.3316 2.5182 2.7196 2.9372 3.1722 3.4259 3.7000 3.9960 4.3157 4.6610 5.0338 5.4365 5.8715 6.3412 6.8485 7.3964 7.9881 8.6271 9.3173 10.0627 10.8677 11.7371 12.6760 13.6901 14.7853 15.9682 17.2456 18.6253 20.1153 21.7245 9%
1.0900 1.1881 1.2950 1.4116 1.5386 1.6771 1.8280 1.9926 2.1719 2.3674 2.5804 2.8127 3.0658 3.3417 3.6425 3.9703 4.3276 4.7171 5.1417 5.6044 6.1088 6.6586 7.2579 7.9111 8.6231 9.3992 10.2451 11.1671 12.1722 13.2677 14.4618 15.7633 17.1820 18.7284 20.4140 22.2512 24.2538 26.4367 28.8160 31.4094 10%
1.1000 1.2100 1.3310 1.4641 1.6105 1.7716 1.9487 2.1436 2.3579 2.5937 2.8531 3.1384 3.4523 3.7975 4.1772 4.5950 5.0545 5.5599 6.1159 6.7275 7.4002 8.1403 8.9543 9.8497 10.8347 11.9182 13.1100 14.4210 15.8631 17.4494 19.1943 21.1138 23.2252 25.5477 28.1024 30.9127 34.0039 37.4043 41.1448 45.2593 11%
1.1100 1.2321 1.3676 1.5181 1.6851 1.8704 2.0762 2.3045 2.5580 2.8394 3.1518 3.4985 3.8833 4.3104 4.7846 5.3109 5.8951 6.5436 7.2633 8.0623 8.9492 9.9336 11.0263 12.2392 13.5855 15.0799 16.7386 18.5799 20.6237 22.8923 25.4104 28.2056 31.3082 34.7521 38.5749 42.8181 47.5281 52.7562 58.5593 65.0009 12%
1.1200 1.2544 1.4049 1.5735 1.7623 1.9738 2.2107 2.4760 2.7731 3.1058 3.4785 3.8960 4.3635 4.8871 5.4736 6.1304 6.8660 7.6900 8.6128 9.6463 10.8038 12.1003 13.5523 15.1786 17.0001 19.0401 21.3249 23.8839 26.7499 29.9599 33.5551 37.5817 42.0915 47.1425 52.7996 59.1356 66.2318 74.1797 83.0812 93.0510 13%
1.1300 1.2769 1.4429 1.6305 1.8424 2.0820 2.3526 2.6584 3.0040 3.3946 3.8359 4.3345 4.8980 5.5348 6.2543 7.0673 7.9861 9.0243 10.1974 11.5231 13.0211 14.7138 16.6266 18.7881 21.2305 23.9905 27.1093 30.6335 34.6158 39.1159 44.2010 49.9471 56.4402 63.7774 72.0685 81.4374 92.0243 103.9874 117.5058 132.7816 14%
1.1400 1.2996 1.4815 1.6890 1.9254 2.1950 2.5023 2.8526 3.2519 3.7072 4.2262 4.8179 5.4924 6.2613 7.1379 8.1372 9.2765 10.5752 12.0557 13.7435 15.6676 17.8610 20.3616 23.2122 26.4619 30.1666 34.3899 39.2045 44.6931 50.9502 58.0832 66.2148 75.4849 86.0528 98.1002 111.8342 127.4910 145.3397 165.6873 188.8835 Math 95 – Homework Unit 1 – Page 8
13. Using the tables, compute the following. Find the…
a. future value of investing $4,000 at 5% annual interest compounded annually for 19 years.
b. future value of investing $8,000 at 24% annual interest compounded monthly for 3 years.
c. future value of investing $8,000 at 24% annual interest compounded monthly for 21 months.
d. future value of investing $5,800 at 10% annual interest compounded semi-annually for 6 years.
e. future value of investing $11,900 at 13% annual interest compounded annually for 27 years.
f. future value of investing $8,300 at 40% annual interest compounded quarterly for 8 years.
Wrap-up and look back:
14. When would you use FV  P1  r  t  instead of FV  P1  i  ? Explain.
nt
15. If using FV  P1  i  as a way to save for retirement, what is the drawback?
nt
16. Would you use FV  P1  i  for a lump sum investment, or for making payments into an account?
nt
17. What are the benefits and drawbacks to the FVIF table? Explain.
18. Is there a difference between 5% annual simple interest and 5% annual interest compounded annually:
a. after one year?
b. after 5 years?
c. after 20 years?
19. Write in words what you learned from this section. Did you have any questions remaining that weren’t
covered in class? Write them out and bring them back to class.
1.3: A Better Way to Save - Annuities
Vocabulary and symbols – write out what the following mean:


Annuity
Future Value Interest Factor Annuity (FVIFA)
Concept questions:
1. Compare and contrast these formulas: FV  pmt

1  i   1
FV  pmt
nt
i
1  i   1 , FV  P1  r  t  , and FV  P1  i 
nt
nt
.
i
2. To get to the same place as investing with a lump sum compound interest account, will the total of all
the payments need to be more than the lump sum, less, or the same? Explain.
Exercises:
3. Try some annuity calculations using the FVIFA tables.
a. If you invest $6,500 each year in an account earning 8% annual interest compounded annually, how
much would you have in 11 years? [$6,500 = max annual contribution to Roth IRA, 50+ yrs old.]
b. If you invest $24,000 each year in an account earning 7% compounded annually, how much would
you have in 18 years? [$24,000 = max annual contribution to a 401k account, 50+ yrs old.]
c. If you invest $80 each month into an account earning 5% annual interest compounded annually,
how much would you have in 25 years? [Hint: make the $80 per month into an annual payment]
d. If you invest $100 each month into an account earning 5% annual interest compounded annually,
how much would you have in 35 years? [Hint: make the $100 per month into an annual payment]
e. According to Edmunds.com, the average monthly payment for a used vehicle is $355 per month for
60 months (5 years). Instead of buying the car, if you invest $355 each month at 7% annual interest
compounded annually, how much would you have in 5 years?
Math 95 – Homework Unit 1 – Page 9
TABLE 2 (Part 1 of 2)
(FVIFA – Future Value Interest Factor Annuity for 1% to 7%)
Periods
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 1%
1.0000 2.0100 3.0301 4.0604 5.1010 6.1520 7.2135 8.2857 9.3685 10.4622 11.5668 12.6825 13.8093 14.9474 16.0969 17.2579 18.4304 19.6147 20.8109 22.0190 23.2392 24.4716 25.7163 26.9735 28.2432 29.5256 30.8209 32.1291 33.4504 34.7849 36.1327 37.4941 38.8690 40.2577 41.6603 43.0769 44.5076 45.9527 47.4123 48.8864 2%
1.0000 2.0200 3.0604 4.1216 5.2040 6.3081 7.4343 8.5830 9.7546 10.9497 12.1687 13.4121 14.6803 15.9739 17.2934 18.6393 20.0121 21.4123 22.8406 24.2974 25.7833 27.2990 28.8450 30.4219 32.0303 33.6709 35.3443 37.0512 38.7922 40.5681 42.3794 44.2270 46.1116 48.0338 49.9945 51.9944 54.0343 56.1149 58.2372 60.4020 3%
1.0000 2.0300 3.0909 4.1836 5.3091 6.4684 7.6625 8.8923 10.1591 11.4639 12.8078 14.1920 15.6178 17.0863 18.5989 20.1569 21.7616 23.4144 25.1169 26.8704 28.6765 30.5368 32.4529 34.4265 36.4593 38.5530 40.7096 42.9309 45.2189 47.5754 50.0027 52.5028 55.0778 57.7302 60.4621 63.2759 66.1742 69.1594 72.2342 75.4013 4%
1.0000 2.0400 3.1216 4.2465 5.4163 6.6330 7.8983 9.2142 10.5828 12.0061 13.4864 15.0258 16.6268 18.2919 20.0236 21.8245 23.6975 25.6454 27.6712 29.7781 31.9692 34.2480 36.6179 39.0826 41.6459 44.3117 47.0842 49.9676 52.9663 56.0849 59.3283 62.7015 66.2095 69.8579 73.6522 77.5983 81.7022 85.9703 90.4091 95.0255 5%
1.0000 2.0500 3.1525 4.3101 5.5256 6.8019 8.1420 9.5491 11.0266 12.5779 14.2068 15.9171 17.7130 19.5986 21.5786 23.6575 25.8404 28.1324 30.5390 33.0660 35.7193 38.5052 41.4305 44.5020 47.7271 51.1135 54.6691 58.4026 62.3227 66.4388 70.7608 75.2988 80.0638 85.0670 90.3203 95.8363 101.6281 107.7095 114.0950 120.7998 6%
1.0000 2.0600 3.1836 4.3746 5.6371 6.9753 8.3938 9.8975 11.4913 13.1808 14.9716 16.8699 18.8821 21.0151 23.2760 25.6725 28.2129 30.9057 33.7600 36.7856 39.9927 43.3923 46.9958 50.8156 54.8645 59.1564 63.7058 68.5281 73.6398 79.0582 84.8017 90.8898 97.3432 104.1838 111.4348 119.1209 127.2681 135.9042 145.0585 154.7620 7%
1.0000 2.0700 3.2149 4.4399 5.7507 7.1533 8.6540 10.2598 11.9780 13.8164 15.7836 17.8885 20.1406 22.5505 25.1290 27.8881 30.8402 33.9990 37.3790 40.9955 44.8652 49.0057 53.4361 58.1767 63.2490 68.6765 74.4838 80.6977 87.3465 94.4608 102.0730 110.2182 118.9334 128.2588 138.2369 148.9135 160.3374 172.5610 185.6403 199.6351 Math 95 – Homework Unit 1 – Page 10
TABLE 2 (Part 2 of 2)
(FVIFA – Future Value Interest Factor Annuity for 8% to 14%)
Periods
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 8%
1.0000 2.0800 3.2464 4.5061 5.8666 7.3359 8.9228 10.6366 12.4876 14.4866 16.6455 18.9771 21.4953 24.2149 27.1521 30.3243 33.7502 37.4502 41.4463 45.7620 50.4229 55.4568 60.8933 66.7648 73.1059 79.9544 87.3508 95.3388 103.9659 113.2832 123.3459 134.2135 145.9506 158.6267 172.3168 187.1021 203.0703 220.3159 238.9412 259.0565 9%
1.0000 2.0900 3.2781 4.5731 5.9847 7.5233 9.2004 11.0285 13.0210 15.1929 17.5603 20.1407 22.9534 26.0192 29.3609 33.0034 36.9737 41.3013 46.0185 51.1601 56.7645 62.8733 69.5319 76.7898 84.7009 93.3240 102.7231 112.9682 124.1354 136.3075 149.5752 164.0370 179.8003 196.9823 215.7108 236.1247 258.3759 282.6298 309.0665 337.8824 10%
1.0000 2.1000 3.3100 4.6410 6.1051 7.7156 9.4872 11.4359 13.5795 15.9374 18.5312 21.3843 24.5227 27.9750 31.7725 35.9497 40.5447 45.5992 51.1591 57.2750 64.0025 71.4027 79.5430 88.4973 98.3471 109.1818 121.0999 134.2099 148.6309 164.4940 181.9434 201.1378 222.2515 245.4767 271.0244 299.1268 330.0395 364.0434 401.4478 442.5926 11%
1.0000 2.1100 3.3421 4.7097 6.2278 7.9129 9.7833 11.8594 14.1640 16.7220 19.5614 22.7132 26.2116 30.0949 34.4054 39.1899 44.5008 50.3959 56.9395 64.2028 72.2651 81.2143 91.1479 102.1742 114.4133 127.9988 143.0786 159.8173 178.3972 199.0209 221.9132 247.3236 275.5292 306.8374 341.5896 380.1644 422.9825 470.5106 523.2667 581.8261 12%
1.0000 2.1200 3.3744 4.7793 6.3528 8.1152 10.0890 12.2997 14.7757 17.5487 20.6546 24.1331 28.0291 32.3926 37.2797 42.7533 48.8837 55.7497 63.4397 72.0524 81.6987 92.5026 104.6029 118.1552 133.3339 150.3339 169.3740 190.6989 214.5828 241.3327 271.2926 304.8477 342.4294 384.5210 431.6635 484.4631 543.5987 609.8305 684.0102 767.0914 13%
1.0000 2.1300 3.4069 4.8498 6.4803 8.3227 10.4047 12.7573 15.4157 18.4197 21.8143 25.6502 29.9847 34.8827 40.4175 46.6717 53.7391 61.7251 70.7494 80.9468 92.4699 105.4910 120.2048 136.8315 155.6196 176.8501 200.8406 227.9499 258.5834 293.1992 332.3151 376.5161 426.4632 482.9034 546.6808 618.7493 700.1867 792.2110 896.1984 1013.7042 14%
1.0000 2.1400 3.4396 4.9211 6.6101 8.5355 10.7305 13.2328 16.0853 19.3373 23.0445 27.2707 32.0887 37.5811 43.8424 50.9804 59.1176 68.3941 78.9692 91.0249 104.7684 120.4360 138.2970 158.6586 181.8708 208.3327 238.4993 272.8892 312.0937 356.7868 407.7370 465.8202 532.0350 607.5199 693.5727 791.6729 903.5071 1030.9981 1176.3378 1342.0251 Math 95 – Homework Unit 1 – Page 11
4. Try some annuity investing on your own using the formula.
a. If you invest 12% of your income and make $4,000 each month, how much will you have in 30
years if you invest at 6% annual interest compounded monthly? Also, determine how much interest
was earned.
b. If you invest 12% of your income and make $4,000 each month, how much will you have in 25
years if you invest at 6% annual interest compounded monthly? Also, determine how much interest
was earned.
c. If you invest 12% of your income and make $4,000 each month, how much will you have in 20
years if you invest at 6% annual interest compounded monthly? Also, determine how much interest
was earned.
d. If you invest 12% of your income and make $4,000 each month, how much will you have in 15
years if you invest at 6% annual interest compounded monthly? Also, determine how much interest
was earned.
e. If you invest 12% of your income and make $4,000 each month, how much will you have in 10
years if you invest at 6% annual interest compounded monthly? Also, determine how much interest
was earned.
f. If you invest 6% of your income and make $4,000 each month, how much will you have in 30 years
if you invest at 6% annual interest compounded monthly? Also, determine the interest earned.
g. If you invest 12% of your $4,000 monthly income for 10 years at 6% annual interest compounded
monthly, and then left it sitting in the account for the next 20 years… how much would you have
total? Also, determine how much interest was earned.
h. Which is better – invest $0 for 10 years then 12% for 20 years or 12% for 10 years and then $0 for
20 years?
5. Invest with Annuities a few more times.
a. If you invest $5,500 each year for a Roth IRA, and you do this for 22 years, how much will be in
the account if it earns 7% annual interest compounded annually. (use the table AND the formula –
this assumes you start investing at age 45 and finish at age 67 so you can retire) Figure out how
much you paid in and how much interest was earned.
b. Someone who is over 50 years old can “catch-up” with extra money into the Roth. If you invest
$6,500 each year for a Roth IRA, and you do this for 17 years (age 50 to 67 only), how much will
be in the account if it earns 7% annual interest compounded annually. (use the table AND the
formula). Figure out how much you paid in and how much interest was earned.
c. If you invest $5,500 each year for a Roth IRA, and you do this for 10 years (from age 30 to age 40),
then stop investing completely. How much would you have at age 67 when you retire? Assume 7%
annual interest compounded annually. Determine how much you paid in and the amount of interest.
d. If you invested $5,500 from age 30 to age 50, then invested $6,500 from age 50 to age 67,
determine how much money you would have in the account. Assume 7% annual interest
compounded annually. Determine how much you paid in and the amount of interest.
Math 95 – Homework Unit 1 – Page 12
6. Work some annuities backwards – find the payment.
a. How much money do you need to invest each month at 5% annual interest compounded monthly for
18 years to end with $60,000 (for your baby’s education)? Determine how much interest you will
earn.
b. How much money do you need to invest each month at 6% annual interest compounded monthly for
32 years to end with $1,000,000 (for your retirement)? Determine how much interest you will earn.
c. Because of extraordinary circumstances, your friend is now 55 years old and hasn’t started saving
for retirement yet. She wants to have $250,000 when she retires at age 70. How much should she
invest each month at 6% annual interest compounded monthly? Determine how much interest she
will earn.
d. Because of extraordinary circumstances, your friend is now 45 years old and hasn’t started saving
for retirement yet. She wants to have $250,000 when she retires at age 70. How much should she
invest each month at 6% annual interest compounded monthly? Determine how much interest she
will earn.
e. Another friend will start investing at age 25 until age 70, how much should she invest each month at
6% annual interest compounded monthly to end with the $250,000? How much more would it cost
her to have $500,000? Or $1,000,000?
7. You could use the FVIFA table to find the payment instead of the future value. Since
1  i   1 becomes FV  pmt FVIFA factor , this shows why we multiply to get the
FV  pmt
nt
i
future value. To undo this, we divide the future value by the FVIFA factor and that will be the
payment!
a. Find the monthly payment that will generate a future value of $35,000 at 24% annual interest
compounded monthly for 3 years. (use the table)
b. Find the annual payment that will generate a future value of $500,000 at 7% annual interest
compounded annually for 30 years. (use the table)
c. Find the annual payment that will generate a future value of $750,000 at 7% annual interest
compounded annually for 40 years. (use the table)
Wrap-up and look back:
1  i   1 for a lump sum investment, or for making payments into an
Would you use FV  pmt
nt
8.
i
account?
9. Based on what we saw in this unit, why is there so much advice to “start investing early”? Explain.
10. Write in words what you learned from this section. Did you have any questions remaining that weren’t
covered in class? Write them out and bring them back to class.
Math 95 – Homework Unit 1 – Page 13
1.4: Dreams Come True – Mortgage/Amortized Loans
Vocabulary and symbols – write out what the following mean:


Amortized Loan
Mortgage

P1  i   pmt
nt
1  i 
nt

1
i
Concept questions:
1. In the formula P1  i nt  pmt
1  i 
2. In the formula P1  i nt  pmt
1  i 
nt
i
nt
 , what does the P1  i 
1
nt
represent?
 , what does the pmt 1  i 
nt
1
 represent?
1
i
i
3. Using the Amortization Factor Table, Shawn is trying to find out the payment on a $35,000 loan at 4%
annual interest compounded monthly for 2 years. He does $3,500 × 43.4249… is this correct? Explain
any errors.
4. While computing the monthly payment P1  i 
nt
1  i 
 pmt
nt
 , David notices that the left portion
1
i
P 1  i  is equal to $1,000,000. Does that mean that if he adds up all his payments, he will pay back
$1,000,000? Explain.
nt
5. Once you have the monthly payment, how can you determine the amount of interest paid?
6. In order to compute the interest on an amortized loan, Charleen uses I  P  r  t . Why will this not
work?
7. Which loan is probably going to default (fail to be paid) more – a shorter loan or a longer loan?
8. Why is the longer loan usually associated with a higher interest rate?
Exercises:
9. Use the formula to find the monthly payment and the amount of interest paid.
a. A mortgage of $455,000 at 3.75% annual interest compounded monthly for 30 years.
b. A student loan of $32,000 at 4.29% annual interest compounded monthly for 10 years.
Math 95 – Homework Unit 1 – Page 14
10. Use the table (Amortization Factor Table) to find the monthly payment of…
a. a home loan for $450,000 at 3% annual interest compounded monthly for 25 years? Then determine
the total amount paid and the amount of interest paid.
b. a home loan for $315,000 at 7% annual interest compounded monthly for 30 years? Then determine
the total amount paid and the amount of interest paid.
c. a home loan for $297,000 at 2% annual interest compounded monthly for 15 years? Then determine
the total amount paid and the amount of interest paid.
d. a car purchased for $29,000 at 4% annual interest compounded monthly for 3 years. What is the
monthly payment? Determine the total amount paid and the amount of interest paid.
e. a car purchased for $29,000 at 4% annual interest compounded monthly for 4 years. What is the
monthly payment? Determine the total amount paid and the amount of interest paid.
f. a car purchased for $29,000 at 4% annual interest compounded monthly for 5 years. What is the
monthly payment? Determine the total amount paid and the amount of interest paid.
g. As we expand the amount of time to pay off the car loan, what happens to (i) the monthly payment
and (ii) the interest paid?
h. The maximum length of time for a car loan is now up to 84 months (7 years). Explain why it is not a
good idea to finance a car over 7 years.
11. Use the formula to determine the amount of loan that will match the information given.
a. You can afford $320 per month for a car; determine how much of a loan amount you can afford for
3 years at 3.25% annual interest compounded monthly. Round loan amount down to the nearest
dollar.
b. You can afford $320 per month for a car; determine how much of a loan amount you can afford for
4 years at 3.35% annual interest compounded monthly. Round loan amount down to the nearest
dollar.
c. You can afford $320 per month for a car; determine how much of a loan amount you can afford for
5 years at 3.45% annual interest compounded monthly. Round loan amount down to the nearest
dollar.
d. You can afford $320 per month for a car; determine how much of a loan amount you can afford for
6 years at 3.65% annual interest compounded monthly. Round loan amount down to the nearest
dollar.
e. You can afford $320 per month for a car; determine how much of a loan amount you can afford for
7 years at 3.95% annual interest compounded monthly. Round loan amount down to the nearest
dollar.
f. Based on the job you plan to have, you know that you can afford a maximum loan payment of $285
per month to pay back your student loans. What is the maximum amount of student loans you could
have at 4.29% annual interest compounded monthly over 10 years (the actual rate for direct
unsubsidized loans for undergraduate students)?
Math 95 – Homework Unit 1 – Page 15
AMORTIZATION FACTOR TABLE 3 – PER $1,000 FINANCED
(1% to 8% compounded monthly)
Months 6 12 18 24 30 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240 252 264 276 288 300 312 324 336 348 360 372 384 396 408 420 432 444 456 468 480 1% 167.1531 83.7854 55.9964 42.1021 33.7656 28.2081 21.2615 17.0937 14.3155 12.3312 10.8432 9.6860 8.7604 8.0032 7.3723 6.8386 6.3812 5.9849 5.6383 5.3325 5.0607 4.8176 4.5989 4.4011 4.2214 4.0573 3.9070 3.7687 3.6412 3.5231 3.4135 3.3115 3.2164 3.1274 3.0441 2.9658 2.8922 2.8229 2.7574 2.6955 2.6369 2.5813 2.5286 2% 167.6402 84.2389 56.4393 42.5403 34.2014 28.6426 21.6951 17.5278 14.7504 12.7674 11.2809 10.1253 9.2013 8.4459 7.8168 7.2850 6.8295 6.4351 6.0903 5.7865 5.5167 5.2756 5.0588 4.8630 4.6852 4.5232 4.3748 4.2385 4.1130 3.9969 3.8893 3.7893 3.6962 3.6092 3.5279 3.4516 3.3800 3.3126 3.2491 3.1892 3.1326 3.0790 3.0283 3% 168.1280 84.6937 56.8843 42.9812 34.6406 29.0812 22.1343 17.9687 15.1937 13.2133 11.7296 10.5769 9.6561 8.9038 8.2779 7.7492 7.2970 6.9058 6.5643 6.2637 5.9972 5.7594 5.5460 5.3534 5.1790 5.0202 4.8751 4.7421 4.6198 4.5070 4.4027 4.3059 4.2160 4.1323 4.0542 3.9811 3.9127 3.8485 3.7882 3.7314 3.6780 3.6275 3.5798 4% 168.6165 85.1499 57.3314 43.4249 35.0833 29.5240 22.5791 18.4165 15.6452 13.6688 12.1893 11.0410 10.1245 9.3767 8.7553 8.2312 7.7835 7.3969 7.0600 6.7639 6.5020 6.2687 6.0598 5.8718 5.7018 5.5475 5.4069 5.2784 5.1605 5.0521 4.9521 4.8597 4.7742 4.6947 4.6208 4.5520 4.4878 4.4277 4.3716 4.3189 4.2695 4.2231 4.1794 5% 169.1056 85.6075 57.7805 43.8714 35.5294 29.9709 23.0293 18.8712 16.1049 14.1339 12.6599 11.5173 10.6066 9.8645 9.2489 8.7306 8.2887 7.9079 7.5768 7.2866 7.0303 6.8028 6.5996 6.4172 6.2528 6.1041 5.9690 5.8459 5.7334 5.6304 5.5357 5.4486 5.3682 5.2939 5.2251 5.1613 5.1020 5.0469 4.9955 4.9476 4.9029 4.8611 4.8220 6% 169.5955 86.0664 58.2317 44.3206 35.9789 30.4219 23.4850 19.3328 16.5729 14.6086 13.1414 12.0057 11.1021 10.3670 9.7585 9.2472 8.8124 8.4386 8.1144 7.8310 7.5816 7.3608 7.1643 6.9886 6.8307 6.6885 6.5598 6.4430 6.3368 6.2399 6.1512 6.0700 5.9955 5.9269 5.8638 5.8055 5.7517 5.7019 5.6558 5.6130 5.5733 5.5364 5.5021 7% 170.0859 86.5267 58.6850 44.7726 36.4319 30.8771 23.9462 19.8012 17.0490 15.0927 13.6337 12.5063 11.6108 10.8841 10.2838 9.7807 9.3540 8.9883 8.6721 8.3966 8.1550 7.9419 7.7530 7.5847 7.4342 7.2992 7.1776 7.0678 6.9684 6.8781 6.7961 6.7213 6.6530 6.5906 6.5334 6.4810 6.4328 6.3886 6.3478 6.3103 6.2757 6.2438 6.2143 8% 170.5771 86.9884 59.1403 45.2273 36.8883 31.3364 24.4129 20.2764 17.5332 15.5862 14.1367 13.0187 12.1328 11.4154 10.8245 10.3307 9.9132 9.5565 9.2493 8.9826 8.7496 8.5450 8.3644 8.2043 8.0618 7.9345 7.8205 7.7182 7.6260 7.5428 7.4676 7.3995 7.3376 7.2815 7.2304 7.1838 7.1414 7.1026 7.0672 7.0348 7.0052 6.9780 6.9531 Math 95 – Homework Unit 1 – Page 16
12. Compare the two loans listed.
a. Compare an add-on interest loan on $150,000 over 10 years at 4% annual simple interest with an
amortized loan for $150,000 over 10 years at 7% annual interest compounded monthly. Analyze the
good and bad of each loan to see which you would prefer and why.
b. Compare an add-on interest loan on $375,000 over 30 years at 3% annual simple interest with an
amortized loan for $375,000 over 30 years at 8.25% annual interest compounded monthly. Analyze
the good and bad of each loan to see which you would prefer and why.
c. Compare an amortized loan on $375,000 over 30 years at 3.75% annual interest compounded
monthly with an amortized loan for $375,000 over 15 years at 2.8% annual interest compounded
monthly. Analyze the good and bad of each loan to see which you would prefer and why.
d. Compare an amortized loan on $32,000 over 3 years at 3.99% annual interest compounded monthly
with an amortized loan for $32,000 over 5 years at 4.49% annual interest compounded monthly.
Analyze the good and bad of each loan to see which you would prefer and why.
13. Business Loans:
a. If a business loan of $420,000 requires quarterly payments, and the interest is 7.7% annual interest
compounded quarterly, how much is the payment if it is to be paid off in 5 years? How much total
will be paid back (principal and interest)?
b. If a business loan of $420,000 requires interest-only monthly for 5 years and then the amount is due
back in full. The interest is 7.7% annual interest compounded monthly, how much is the monthly
interest-only payment? How much total will be paid back?
c. If a business takes an add-on interest loan of $420,000. It is a loan for 5 years and the interest is
7.7% annual simple interest, how much is the monthly payment? How much total will be paid
back?
d. Compare the 3 options. What are the good and bad of each?
14. Determine the amount to be paid each month to pay off the balance.
a. If the car loan has a balance of $8,900 and the interest rate is 6.8% annual interest compounded
monthly, what is the amount needed to be paid each month to have this paid off in 4 years?
b. If the car loan has a balance of $8,900 and the interest rate is 6.8% annual interest compounded
monthly, what is the amount needed to be paid each month to have this paid off in 18 months?
c. How much interest is saved from (a) to (b) – paying the car loan off in 2.5 fewer years?
d. If the home loan has a balance of $238,900 and the interest rate is 3.8% annual interest compounded
monthly, what is the amount needed to be paid each month to have this paid off in 12 years?
e. If the home loan has a balance of $238,900 and the interest rate is 3.8% annual interest compounded
monthly, what is the amount needed to be paid each month to have this paid off in 10 years?
f. How much interest is saved from (d) to (e) – paying the mortgage off in 2 fewer years?
g. A credit card has a balance of $3,215 and your friend wants to pay it off over 3 years. The interest
rate is 17.99% annual interest compounded monthly – what monthly payment is needed?
h. A credit card has a balance of $3,215 and your friend wants to pay it off over 1 year. The interest
rate is 17.99% annual interest compounded monthly – what monthly payment is needed?
i. How much interest is saved from (g) to (h) – paying the credit card in 2 fewer years?
Math 95 – Homework Unit 1 – Page 17
Wrap-up and look back:
15. True/False (explain if your answer is false):
a. Add-on interest loans charge interest on the remaining balance.
b. Amortized loans charge interest on the remaining balance.
c. Amortized loans charge interest on the loan amount only.
d. Add-on interest loans have equal monthly payments.
e. The interest paid on amortized loans is calculated with I  P  r  t .
f. The interest paid on add-on interest loans is calculated with I  P  r  t .
g. Paying extra on amortized loans will save you time.
h. Paying extra on amortized loans will save you money.
i. Paying extra on add-on interest loans will save you time.
j. Paying extra on add-on interest loans will save you money.
16. Why is it sometimes better to take an amortized loan with a higher interest rate than an add-on interest
loan with a lower interest rate?
17. Write in words what you learned from this section. Did you have any questions remaining that weren’t
covered in class? Write them out and bring them back to class.
1.5: The Trouble with Compound Interest (Mortgages)
Vocabulary and symbols – write out what the following mean:



P & I payment
Amortiation Schedule
Unpaid Balance

UB  P1  i 
k
1  i   1
 pmt
k
i
Concept questions:
1. Why is the total payment on a mortgage not the same as the P & I payment?
2. In the unpaid balance formula, why is the exponent k instead of nt?
k
3. In the unpaid balance formula, what does the P 1  i  portion relate to?
1  i   1 portion relate to?
k
4. In the unpaid balance formula, what does the pmt
i
5. Why do we round the P & I payment up to the nearest penny?
6. Why is the loan not paid off exactly after making equal payments for the length of the term?
7. In an amortized loan, does the amount you pay to interest stay the same each month? Why or why not?
8. In an amortized loan, does the amount you pay to interest in the first month match the amount paid to
interest in the final month? Why or why not?
Math 95 – Homework Unit 1 – Page 18
Exercises:
9. Determine (i) the monthly P & I payment, (ii) the amount of interest paid in the first month, and (iii) the
amount of the first P & I payment that goes to pay off the remaining balance.
a. A mortgage for $475,000 at 4.25% annual interest compounded monthly for 30 years.
b. A mortgage for $475,000 at 4.25% annual interest compounded monthly for 15 years.
c. Why is the interest paid in the first month the same for (a) and (b)?
d. A car loan for $29,000 at 7.25% annual interest compounded monthly for 3 years.
e. A car loan for $29,000 at 7.25% annual interest compounded monthly for 6 years.
f. In (d) the amount of time is half as long as the loan in (e). How does the payment compare – is it
half as much?
10. For these questions, (i) determine the monthly payment on the loan, (ii) use the unpaid balance formula
use an amortization
to approximate the unpaid balance after 3 years, then (iii)
schedule/spreadsheet to find the unpaid balance after 3 years on…
a. A mortgage on $347,500 at 4.55% annual interest compounded monthly for 30 years.
b. A mortgage on $347,500 at 4.25% annual interest compounded monthly for 15 years.
c. A car loan on $37,500 at 9.34% annual interest compounded monthly for 5 years.
d. A car loan on $37,500 at 9.34% annual interest compounded monthly for 7 years.
e. A student loan on $87,500 at 4.29% annual interest compounded monthly for 10 years.
f. Is the formula the same as the amount found on the spreadsheet for the unpaid balance?
11. Refer to the previous problem and compute (i) the unpaid balance after 8 years if the initial P&I
payment is made and (ii) the unpaid balance after 8 years if the P&I payment is increased by $150 per
month for
a. A mortgage on $347,500 at 4.55% annual interest compounded monthly for 30 years.
b. A mortgage on $347,500 at 4.25% annual interest compounded monthly for 15 years.
12. 12 years ago, Howard took a 30-year mortgage loan for $568,000 at 5.45% annual interest compounded
monthly. He paid the minimum payment each month and never missed a payment. However, he just
received an inheritance of $300,000 and wants to pay off the loan completely.
a. Does he have enough to pay it off or not?
b. If he invests the $300,000 instead of putting it towards the house, and if Howard continues paying
on his amortized loan for 15 total years (half the time), will he have paid off half the loan or not?
Explain.
How long will it take for his loan to be paid off half way? (use an amortization schedule on the
computer)
d. If he added $200 to his payments (for the first 12 years of the loan), how long until the loan was
paid off halfway?
c.
Math 95 – Homework Unit 1 – Page 19
13.
12 years ago, Howard took a 30-year mortgage loan for $568,000 at 5.45% annual interest
compounded monthly. He paid the minimum payment each month and never missed a payment.
However, he just received an offer to refinance the home. There is a fee of 2% of the remaining balance
for this offer, but the interest rate will be 4.25% and he could refinance for 30 years, or he could take
3.75% and refinance for 15 years. Analyze all options to see which is best for Howard – stay with
current, refi for 30, refi for 15, refi but make current payment still, etc. Explain why. The computer is
strongly recommended here for analysis.
14. Yulemi is considering two mortgages on her loan amount of $403,500. The first is a 30 year mortgage
at 5.15% annual interest compounded monthly and the second is a 15 year mortgage at 4.48% annual
interest compounded monthly. Compare these options and determine which is best for her:
a. She takes the 30 year option and makes the 30 year P & I payment for 30 years.
b. She takes the 15 year option and makes the 15 year P & I payment for 15 years.
c. She takes the 30 year option and makes the 15 year P & I payment until paid off.
Wrap-up and look back:
15. Why is it sometimes better to take the 30 year loan over a 15 year loan?
16. Why is it sometimes better to take the 15 year loan over a 30 year loan?
17. Which one will typically have a higher interest rate: a 15 year loan or a 30 year loan?
18. Write in words what you learned from this section. Did you have any questions remaining that weren’t
covered in class? Write them out and bring them back to class.
1.6: The Joys of Compound Interest (Retirement)
Vocabulary and symbols – write out what the following mean:


Time Value of Money
Payout Annuity

P1  i 
nt
1  i 
 pmt
nt

1
i
Concept questions:
1. If we only took out the interest from a retirement account, how long would the account last?
2. Jonathan doesn’t like investing money and so he will stockpile money away for retirement in a
fireproof safe in his house – earning no interest at all.
a. If Jonathan wanted to be paid $2,500 each month when he retired, how much money would he need
for the payouts to last for 20 years?
b. If Jonathan wanted to invest over the 35 years prior to retirement, how much would he need to put
away each month to end with the amount in part (a)?
c. If he ended up changing his mind and investing in an account that earned 3.25% interest during
retirement and 5.5% interest during the investment phase…
i. How much would he need at retirement to have enough for a payout annuity that would pay
$2,500 each month for 20 years?
ii. How much would he need to invest over 35 years to have the amount in (i)?
d. Why is investing, even with low interest rates, better than with none at all?
Math 95 – Homework Unit 1 – Page 20
3. If we computed that we can take out $1,400 each month for the money to last 20 years, will the money
last more, less, or just 20 years if we take out…
b. $2,000 each month.
c. $1,400 each month.
a. $1,300 each month.
Exercises:
4. Michael knows that he needs $3,100 per month to live comfortably now. He plans to retire in about 34
years and plans to be retired for about 18 years after that. Determine…
a. how much he needs each month to maintain his current standard of living when he retires 34 years
from now (assuming 2.5% inflation).
b. how much he needs to have in his retirement account to be paid out equal monthly amounts of the
amount in (a) each month for 18 years if the account earns 5% annual interest compounded
monthly.
c. how much he needs to invest each month at 7% annual interest compounded monthly over the next
34 years in order to have the amount in (b).
d. how much interest he earned over the course of the 52 years.
5. Elizabeth knows that she needs $3,700 per month to live comfortably now. She plans to retire in about
39 years and plans to be retired for about 23 years after that. Determine…
a. how much she needs each month to maintain her current standard of living when she retires 39
years from now (assuming 3.1% inflation).
b. how much she needs to have in his retirement account to be paid out equal monthly amounts of the
amount in (a) each month for 23 years if the account earns 5% annual interest compounded
monthly.
c. how much she needs to invest each month at 7% annual interest compounded monthly over the next
39 years in order to have the amount in (b).
d. how much interest she earned over the course of the 62 years.
6. Abbielee Mueller knows that she needs $2,900 per month to live comfortably now. However, she hasn’t
started saving for retirement and she is 50 years old! She plans to retire in about 20 years and plans to
be retired for about 15 years after that. Determine…
a. how much she needs each month to maintain her current standard of living when she retires 20
years from now (assuming 3.1% inflation).
b. how much she needs to have in his retirement account to be paid out equal monthly amounts of the
amount in (a) each month for 15 years if the account earns 5% annual interest compounded
monthly.
c. how much she needs to invest each month at 7% annual interest compounded monthly over the next
20 years in order to have the amount in (b).
d. how much interest she earned over the course of the 35 years.
7. Determine some information with payout annuities.
a. Jon Snow wants to be paid out $3,500 per month over the next 25 years. How much does he need to
invest to make this payout happen (both investments use 5.25% annual interest compounded
monthly)?
b. Arya Stark wants to be paid out $3,500 per month over the next 25 years. How much does she need
to invest to make this payout happen (both investments use 6.75% annual interest compounded
monthly)?
Math 95 – Homework Unit 1 – Page 21
c. Sansa Stark wants to be paid out $8,750 per month when retired. She will retire 25 years from now
and plans to be retired for 15 years. Her investments all earn 6.15% annual interest compounded
monthly.
i. How much will she need to invest at retirement to guarantee 15 years of payouts?
ii. How much will she need to invest each month for the next 25 years of work?
iii. How much interest will she earn over the 40 years total?
iv. If Sansa had some cash now, as a wedding gift from Petyr Baelish, and she wanted to invest
this lump sum instead of making monthly payments, how much would she need to invest to
get to the retirement amount in (i)?
v. How much total interest would she earn over the 40 years if she chose this option?
8. Practice a few times to find (i) the amount of the cash prize in a lottery and (ii) the amount that the
winner would actually claim for taking the cash prize after the 39.6% federal tax bill…
a. for a $3 million lottery, assuming 4% annual interest compounded annually and that the prize is
paid out at the same amount each year for 25 years.
b. for a $3 million lottery, assuming 5% annual interest compounded annually and that the prize is
paid out at the same amount each year for 25 years
c. for a $6 million lottery, assuming 2.5% annual interest compounded annually and that the prize is
paid out at the same amount each year for 25 years
d. for a $24 million lottery, assuming 2.5% annual interest compounded annually and that the prize is
paid out at the same amount each year for 25 years.
e. for a $24 million lottery, assuming 2.5% annual interest compounded annually and that the prize is
paid out at the same amount each year for 30 years.
f. for a $40 million lottery, assuming 2.85% annual interest compounded annually and that the prize is
paid out at the same amount each year for 30 years.
g. for a $903 million lottery, assuming 3.25% annual interest compounded annually and that the prize
is paid out at the same amount each year for 30 years.
h. for a $903 million lottery, assuming 5.4% annual interest compounded annually and that the prize is
paid out at the same amount each year for 30 years.
Wrap-up and look back:
9. If the interest rate is lower, do we need to invest more or less money to guarantee the payouts? Why?
10. Is the cash prize higher or lower if the interest rate decreases? Explain why.
11. Why is it so important to use inflation rates to determine monthly payments at retirement?
12. If you had to choose between monthly payment investing for retirement and lump sum investing, which
would…
a. be easier for you to handle?
b. earn more interest?
c. have a larger amount of total cash needed?
13. Explain why the cash prize for a lottery is so much less than the listed annuity prize.
14. If the annuity and cash prizes were close in value, would you suspect high interest rates or low interest
rates for the state? Why?
Math 95 – Homework Unit 1 – Page 22
15. If someone won the lottery, give reasons for taking the cash prize as well as reasons for taking the
annuity.
16. Write in words what you learned from this section. Did you have any questions remaining that weren’t
covered in class? Write them out and bring them back to class.
1.7: COLA, but not soda
Vocabulary and symbols – write out what the following mean:

Cost of Living Adjustment

  1  c t
1 

 1 r 
P  pmt 
r c










Concept questions:
1. Why does the cost of living change over time?
2. Why is there a problem with receiving fixed payments over time?
3. Bertha is thinking of investing in an annuity to last for 20 years with an initial payment of $32,000,
with COLA of 2% and rate of 5.9% annual interest compounded annually. Marlesha is thinking of
investing in an annuity to last for 20 years with an initial payment of $32,000, with COLA of 2% and
rate of 4.9% annual interest compounded annually. Without doing any computations, determine who
should have a bigger up-front cost?
4. Buddy is thinking of investing in an annuity to last for 20 years with an initial payment of $32,000,
with COLA of 3% and rate of 5.9% annual interest compounded annually. Manny is thinking of
investing in an annuity to last for 20 years with an initial payment of $32,000, with COLA of 2% and
rate of 5.9% annual interest compounded annually. Without doing any computations, determine who
should have a bigger up-front cost?
5. Which of these accounts will need a larger initial investment:
a. an account that earns 5% annual interest with 2% COLA.
b. an account that earns 5% annual interest with 3% COLA.
6. Which of these accounts will need a larger initial investment:
a. an account that earns 7% annual interest with 2% COLA.
b. an account that earns 5% annual interest with 2% COLA.
Exercises:
7. If the first payment from a COLA payout annuity is $25,000, and the COLA is 3%, determine…
d. The amount of the 10th payment.
a. The amount of the 1st payment.
b. The amount of the 2nd payment.
e. The amount of the 21st payment.
rd
c. The amount of the 3 payment.
f. The amount of the 31st payment.
Math 95 – Homework Unit 1 – Page 23
8. If the first payment from a COLA payout annuity is $25,000, and the COLA is 2.3%, determine…
d. The amount of the 10th payment.
a. The amount of the 1st payment.
b. The amount of the 2nd payment.
e. The amount of the 21st payment.
rd
c. The amount of the 3 payment.
f. The amount of the 31st payment.
9. If the first payment from a COLA payout annuity is $25,000, and the COLA is 3.5%, determine…
d. The amount of the 10th payment.
a. The amount of the 1st payment.
nd
b. The amount of the 2 payment.
e. The amount of the 21st payment.
c. The amount of the 3rd payment.
f. The amount of the 31st payment.
10. Using the COLA payout annuity formula, determine the amount of money needed if…
a. The annuity is to last for 25 years with an initial payment of $32,000, with COLA of 3% and rate of
5.9% annual interest compounded annually.
b. The annuity is to last for 20 years with an initial payment of $32,000, with COLA of 3% and rate of
5.9% annual interest compounded annually.
c. The annuity is to last for 20 years with an initial payment of $32,000, with COLA of 2% and rate of
5.9% annual interest compounded annually.
d. The annuity is to last for 20 years with an initial payment of $32,000, with COLA of 2% and rate of
4.9% annual interest compounded annually.
e. The annuity is to last for 15 years with an initial payment of $32,000, with COLA of 2% and rate of
5.9% annual interest compounded annually.
11. You can use the COLA formula for monthly payments instead of annual, but the interest must be the
periodic rate (using compounded monthly) and the COLA must be monthly as well. EX: if the annual
COLA was 4.8%, then the monthly would be 4.8% ÷ 12 = 0.4%. Using the COLA payout annuity
formula, determine the amount of money needed if…
a. The annuity is to last for 25 years with an initial monthly payment of $2,000, with monthly COLA
of 0.3% and rate of 6.0% annual interest compounded monthly.
b. The annuity is to last for 20 years with an initial monthly payment of $2,500, with monthly COLA
of 0.3% and rate of 5.4% annual interest compounded monthly.
c. The annuity is to last for 20 years with an initial monthly payment of $2,500, with monthly COLA
of 0.25% and rate of 4.8% annual interest compounded monthly.
d. The annuity is to last for 15 years with an initial monthly payment of $3,800, with monthly COLA
of 0.25% and rate of 4.8% annual interest compounded monthly.
e. The annuity is to last for 20 years with an initial monthly payment of $7,800, with monthly COLA
of 0.35% and rate of 7.2% annual interest compounded monthly.
f. The annuity is to last for 25 years with an initial monthly payment of $9,800, with monthly COLA
of 0.35% and rate of 7.2% annual interest compounded monthly.
12.
Marjorie Tyrell has $272,319 in her retirement account. Use a spreadsheet to determine these
results. If she earns 4.7% annual interest compounded annually, how long would the payments last if
she pulled out a …
a. A fixed annual payment of $48,000.
b. A first annual payment of $48,000 with an annual COLA of 3%.
c. A first annual payment of $48,000 with an annual COLA of 4%.
Math 95 – Homework Unit 1 – Page 24
13. Lucille has $272,319 in her retirement account. Use the formula to determine how much she can get as
an annual payment if she wants…
a. fixed payments for 20 years and will earn 7% annual interest compounded annually.
b. annual payments for 20 years with an annual COLA of 3.2% earning the same interest as (a).
c. which of these would you recommend for Lucille and why?
14. In order to determine the total amount paid out from a COLA payout annuity, we can use a formula
1  i nt  1 . When using this formula, the pmt is the first payment made
we’ve seen before: FV  pmt
i
and the periodic rate is computed using the COLA rate, not the interest rate. The future value will be
the sum of all the payments! Determine the amount paid out of these COLA payout annuities:
a. First payment of $39,500 with cost of living as 2.8% and interest of 5.75% annual interest
compounded annually, over 20 years.
b. First payment of $89,500 with cost of living as 2.5% and interest of 6.15% annual interest
compounded annually, over 25 years.
c. First payment of $139,500 with cost of living as 3.1% and interest of 4.75% annual interest
compounded annually, over 13 years.
d. First payment of $817,400 with cost of living as 1.9% and interest of 6.99% annual interest
compounded annually, over 30 years.
e. First payment of $41,500 with cost of living as 2.8% and interest of 5.75% annual interest
compounded annually, for 9 years.
f. First payment of $41,500 with cost of living as 2.8% and interest of 5.75% annual interest
compounded annually, for 19 years.


17. Napolean Dynamite knows that he needs $3,100 per month to live comfortably now. He plans to retire
in about 34 years and plans to be retired for about 18 years after that. Determine…
a. how much he needs each month to maintain his current standard of living when he retires 34 years
from now (assuming 2.4% inflation).
b. how much he needs to have in his retirement account to be paid out monthly amounts that start with
the amount in (a) but increase by the 2.4% annual inflation each month for 18 years if the account
earns 5.1% annual interest compounded monthly.
c. how much he needs to invest each month at 7% annual interest compounded monthly over the next
34 years in order to have the amount in (b).
d. how much he will be paid out of the COLA payout annuity.
e. how much interest he earned over the course of the 52 years.
18. Jacquelyn knows that she needs $3,700 per month to live comfortably now. She plans to retire in about
39 years and plans to be retired for about 23 years after that. Determine…
a. how much she needs each month to maintain her current standard of living when she retires 39
years from now (assuming 3.6% inflation).
b. how much she needs to have in her retirement account to be paid out monthly amounts that start
with the amount in (a) but increase by the 3.6% annual inflation each month for 23 years if the
account earns 6% annual interest compounded monthly.
c. how much she needs to invest each month at 7% annual interest compounded monthly over the next
39 years in order to have the amount in (b).
d. how much she will be paid out of the COLA payout annuity.
e. how much interest she earned over the course of the 62 years.
Math 95 – Homework Unit 1 – Page 25
19. Consider the previous problem and determine how much she would need to invest if the payments were
going to be fixed monthly payments instead of COLA.
a. Compare this with the previous information – is it true that she pays more with the COLA account?
b. How much more is her monthly payment while preparing for retirement?
c. Which option is better for her?
20. Powerball/MegaMillions COLA payments over 30 years. For a Powerball jackpot of $180,000,000,
determine…
a. the first payment if the annuity is chosen.
b. the cash prize if the interest rate is 2.55% annual interest compounded annually.
c. the amount the winner would get if the cash prize is taken and then charged a tax rate of 39.6%
(Federal income tax).
21. Powerball/MegaMillions COLA payments over 30 years. For a Powerball jackpot of $903,000,000,
determine…
a. the first payment if the annuity is chosen.
b. the cash prize if the interest rate is 3.25% annual interest compounded annually.
c. the amount the winner would get if the cash prize is taken and then charged a tax rate of 39.6%
(Federal income tax).
22. If you had to choose between COLA payments for lottery winnings and fixed payments, which one
would you prefer?
23. If you had to choose between COLA payments for lottery winnings and the cash prize, which one
would you prefer?
Wrap-up and look back:
24. What are you risking by choosing the cash prize for a lottery instead of the COLA payments?
25. What are you risking by choosing the COLA payments for a lottery instead of the cash prize?
26. If you were saving for your own retirement, would you want to do flat payments (previous section) or
the COLA payments (this section). Explain why.
27. If investing at 5% annual interest compounded annually,
28. Write in words what you learned from this section. Did you have any questions remaining that weren’t
covered in class? Write them out and bring them back to class.
1.8: Everyone Loves a Log, You’re going to Love a Log!
Vocabulary and symbols – write out what the following mean:


Logarithm
Doubling Time


P i 

log1 
pmt 

k 
log1  i 
Math 95 – Homework Unit 1 – Page 26
Concept questions:
1. The logarithm represents an exponent – true or false?
2. We use logarithms when solving an equation for the exponent – true or false?
3. How can you rewrite 145  10 x using logarithms?
4. Does the length of time needed to double our money depend on the initial investment, the interest rate,
or both?
5. When we use a calculator to solve for a logarithm, is the result an exact value or an approximation?
6. When we check our answer using the calculator, will the value be exact or approximate?
Exercises:
7. Solve the following equations using your calculator. If the answer is not exact, round to 4 decimal
places. Be sure to check your work with each one.
a. 12n  248,832
d. 1.0625n  3.21
n
b. 501.05  400
c. 5001.04 n  12,000
e. 200.98n  13.2
f.
60.8  2.4576
n
8. Determine how long it would take for the present value to become the future value.
a. How long until $30,000 becomes $60,000 at 4.5% annual interest compounded monthly?
b. How long until $50,000 becomes $100,000 at 4.5% annual interest compounded monthly?
c. How long until $50,000 becomes $200,000 if the rate is 4.5% annual interest compounded
monthly?
d. The time in (c) is twice as long as in (b). Explain why this makes sense.
e. How long to turn $7,300 into $25,000 if the rate is 6.5% annual interest compounded monthly?
f. How long to turn $7,300 into $25,000 if the rate is 6.5% annual interest compounded annually?
9. Hamlet has $60,000 to invest, and wants to turn it into $1,000,000. How many years will it take for this
to happen if he invests at…
a. 5% annual interest compounded monthly?
b. 5% annual interest compounded annually?
c. 5% annual interest compounded weekly?
d. 5% annual interest compounded daily?
e. 5% annual interest compounded 1,000 times per year?
f. 5% annual interest compounded 100,000 times per year?
g. 5% annual interest compounded 100,000,000 times per year?
10. Use the rule of 70 to estimate how long it will take money to double with the interest rates listed below:
c. 14%
e. 11%
a. 5%
b. 10%
d. 8.9%
f. 3%
11. Compute the following information about doubling time (use the formula, not the rule of 70).
Math 95 – Homework Unit 1 – Page 27
a. How long does it take your money to double if you invest at 6% annual interest compounded
monthly?
b. If you start with $10,000, and put it in the account in part (a) for the time you discovered, how
much will the account have in it?
c. Now take the same $10,000 and put it in the account in part (a), but this time for half the time you
found in (a). Are you halfway to doubling your money?
d. Repeat parts (a) through (c) using 3% annual interest compounded monthly.
e. Repeat parts (a) through (c) using 12% annual interest compounded daily.
f. Repeat parts (a) through (c) using 7.85% annual interest compounded weekly.
12. There is a famous problem about a biology lab that has a jar with bacteria in it. The number of bacteria
double every minute, and the jar will be full at 11:00 am. If it is 10:00 am now, how full is the jar at…
a. 10:59 am?
b. 10:58 am?
c. How many jars are needed to keep all the bacteria at:
iii. 11:04 am
i. 11:00am
ii. 11:01 am
iv. 11:10 am.

P i 

log1 
pmt 

13. Use the formula k  
to see how long it would take to pay off the given debts.
log1  i 
a. How long would it take to pay off a student loan of $98,000 if you can only afford monthly
payments of $350 and the interest rate is 4.89% annual interest compounded monthly?
b. How long would it take to pay off a mortgage of $484,000 if you can suddenly afford monthly
payments of $2,900 and the interest rate is 4.73% annual interest compounded monthly?
c. How long would it take to pay off a credit card balance of $2,172 if you can only afford monthly
payments of $75 and the interest rate is 18.99% annual interest compounded monthly?
d. How long would it take to pay off a credit card balance of $2,172 if you can only afford monthly
payments of $75 and the interest rate is 4.99% annual interest compounded monthly?
Wrap-up and look back:
14. If the doubling time for a particular interest rate is 7 years, how long will it take $20,000 to become…
c. $160,000
a. $40,000
b. $80,000
d. $320,000
15. Why does half the doubling time not result in ending halfway to the doubled investment?
16. Write in words what you learned from this section. Did you have any questions remaining that weren’t
covered in class? Write them out and bring them back to class.
1.9: A Taxing Dilemma
Vocabulary and symbols – write out what the following mean:


Adjusted Gross Income (AGI)
Taxable Income (TI)


Tax
Deductions
Math 95 – Homework Unit 1 – Page 28



Exemptions
Withheld
Tax Bracket



Tax Refund
MFJ
HoH
Concept questions:
1. With taxes, does the AGI come before or after the TI?
2. If you were in the 25% tax bracket, then a deduction of $10,000 would save how much in tax?
3. If you were in the 25% tax bracket, then a deduction of $1,000 would save how much in tax?
4. If you were in the 15% tax bracket, then a credit of $1,000 would save how much in tax?
5. If you were in the 25% tax bracket, then a deduction of $8,000 would be equivalent to how much of a
tax credit?
6. If someone is in the 25% tax bracket, does that mean they pay 25% tax on all their income?
7. Interpret what it means to be in the 28% tax bracket if you are filing as single? Is that different than if
you are filing as MFJ?
8. Luis and Luisa are trying to claim their daughter on their taxes for one more year. If they are in the 25%
tax bracket, how much will they save in taxes?
9. Matt and Mary are trying to claim their daughter on their taxes for one more year. If they are in the
15% tax bracket, how much will they save in taxes?
10. Richard and Rhee are trying to claim their daughter on their taxes for one more year. If they are in the
39.6% tax bracket, how much will they save in taxes?
Math 95 – Homework Unit 1 – Page 29
Exercises:
Graduated tax system (IRS) based on 2015 tax code – METHOD 1 (Addition):
Individual Taxpayers (Single)
If Taxable Income is Between
The tax due is
Plus this percent
Of the amount over
0 and $9,225
0
10%
0
$9,226 and $37,450
$922.50
15%
$9,225
$37,451 and $90,750
$5,156.25
25%
$37,450
$90,751 and $189,300
$18,481.25
28%
$90,750
$189,301 and $411,500
$46,075.25
33%
$189,300
$411,501 and $413,200
$119,401.25
35%
$411,500
$413,201 and above
$119,996.25
39.6%
$413,200
If Taxable Income is Between
0 and $18,450
$18,451 and $74,900
$74,901 and $151,200
$151,201 and $230,450
$230,451 and $411,500
$411,501 and $464,850
$464,851 and above
Married Filing Jointly (MFJ)
The tax due is
Plus this percent
0
10%
$1,845
15%
$10,312.50
25%
$29,387.50
28%
$51,577.50
33%
$111,324.00
35%
$129,996.50
39.6%
Of the amount over
0
$18,450
$74,900
$151,200
$230,450
$411,500
$464,850
If Taxable Income is Between
0 and $13,150
$13,151 and $50,200
$50,201 and $129,600
$129,601 and $209,850
$209,851 and $411,500
$411,501 and $439,000
$439,001 and above
Head of Household (HoH)
The tax due is
Plus this percent
0
10%
$1,315.00
15%
$6,872.50
25%
$26,772.50
28%
$49,192.50
33%
$115,737.00
35%
$125,362.00
39.6%
Of the amount over
0
$13,150
$50,200
$129,600
$209,850
$411,500
$439,000
We will not include Married Filing Separately for space reasons only. Deductions/exemptions are below:
Single
MFJ
HoH
Standard Deduction
$6,300
$12,600
$9,250
Exemptions
$4,000 per exemption
Math 95 – Homework Unit 1 – Page 30
Graduated tax system (IRS) based on 2015 tax code – METHOD 2 (Subtraction):
NOTE: This table is used for taxable income over $100,000 – lower amounts are done with a tax table.
Individual Taxpayers (Single)
If Taxable Income (TI) is
Take TI Times this percent
At least $100,000 but not over $189,300
28%
Over $189,300 but not over $411,500
33%
Over $411,500 but not over $413,200
35%
Over $413,200
39.6%
Then subtract this
$6,928.75
$16,393.75
$24,623.75
$43,630.95
Married Filing Jointly (MFJ)
If Taxable Income (TI) is
Take TI Times this percent
At least $100,000 but not over $151,200
25%
Over $151,200 but not over $230,450
28%
Over $230,450 but not over $411,500
33%
Over $411,500 but not over $464,850
35%
Over $464,850
39.6%
Then subtract this
$8,412.50
$12,948.50
$24,471.00
$32,701.00
$54,084.10
Head of Household (HoH)
If Taxable Income (TI) is
Take TI Times this percent
At least $100,000 but not over $129,600
25%
Over $129,600 but not over $209,850
28%
Over $209,850 but not over $411,500
33%
Over $411,500 but not over $439,000
35%
Over $439,000
39.6%
Then subtract this
$5,677.50
$9,565.50
$20,058.00
$28,288.00
$48,482.00
11. Use whichever table you prefer to calculate the tax owed on a taxable income of $430,000 if you file…
b. MFJ
c. HoH
a. Single
12. Use whichever table you prefer to calculate the tax owed on a taxable income of $230,000 if you file…
b. MFJ
c. HoH
a. Single
13. Use whichever table you prefer to calculate the tax owed on a taxable income of $150,000 if you file…
b. MFJ
c. HoH
a. Single
14. Use whichever table you prefer to calculate the tax owed on a taxable income of $58,000 if you file…
b. MFJ
c. HoH
a. Single
15. Scenario: Ivana Trump has income of $48,600 and will file as single. She took a new job and had
moving expenses of $780 which is put in as an income adjustment (before AGI). She also finished up
her school and has some education expenses so that she could take either $4,000 as a tuition/fees
deduction or $2,000 as an education tax credit. She had $9,336 withheld from her paychecks for taxes.
a. Consider the deduction scenario and run through the tax scenario. How much tax will she pay in
this scenario? Does she get a refund; if so, how much?
b. Consider the tax credit scenario and run through the tax scenario. Remember that credits are
removed from taxes after the tax is calculated. How much tax will she pay with this scenario? Will
she get a refund? If so, how much?
c. Which option is better for Ivana – tax deduction for school, or education tax credit?
d. Determine the ratio of tax paid to gross income for the best option for Ivana, and turn into a
percentage. Is this the same percentage as the tax bracket she was in? Explain.
Math 95 – Homework Unit 1 – Page 31
16. Scenario: Shawna has income of $78,600 and will file as MFJ with her husband. He is unemployed and
going to school, and has some education expenses so that they could take either $4,000 as a tuition/fees
deduction or $2,000 as an education tax credit. They have 2 kids and each qualifies for a $1,000 child
tax credit. She had $8,521 withheld from her paychecks for taxes.
a. Consider the deduction scenario and run through the tax scenario. Remember, deductions are
subtracted prior to AGI. How much tax will they pay with this scenario? Will they get a refund? If
so, how much?
b. Consider the tax credit scenario and run through the tax scenario. Remember that credits are
removed from taxes after the tax is calculated. How much tax will they pay with this scenario? Will
they get a refund? If so, how much?
c. Which option is better for Shawna’s family – tax deduction for school, or tax credit?
d. Determine the ratio of tax paid to gross income for the best option for Shawna’s family, and turn
into a percentage. Is this the same percentage as the tax bracket she was in? Explain.
17. Ben Higgins is filling out his taxes for 2015. He has income of $83,500 and is deciding whether or not
to get married during 2015. If so, he can claim MFJ status instead of single. His fiancée, Amanda, has
income of $45,300 and does have 2 kids (each qualifying for the $1,000 child credit). Both will take the
standard deduction either way. The total amount withheld for federal taxes was $13,563 for him and
$1,812 for her.
a. Consider Ben filing as single and not getting married in 2015. How much tax will he pay with this
scenario? Will he get a refund? If so, how much?
b. Consider Amanda filing as HoH and not getting married in 2015. How much tax will she pay with
this scenario? Will she get a refund? If so, how much?
c. Consider the two getting married at the end of 2015 and filing as MFJ. How much tax will they pay
with this scenario? Will they get a refund? If so, how much?
d. Which option is better – marriage or not? Explain.
e. Would you consider this a marriage bonus or a marriage penalty? Why?
18. Rob Stark is filling out his taxes for 2015. He has income of $83,500 and is deciding whether or not to
get married during 2015. If so, he can claim MFJ status instead of single. His fiancée, Talisa, has
income of $95,300. Both will take the standard deduction either way. The total amount withheld for
federal taxes was $10,563 for him and $11,812 for her.
a. Consider Rob filing as single and not getting married in 2015. How much tax will he pay with this
scenario? Will he get a refund? If so, how much?
b. Consider Talisa filing as HoH and not getting married in 2015. How much tax will she pay with this
scenario? Will she get a refund? If so, how much?
c. Consider the two getting married at the end of 2015 and filing as MFJ. How much tax will they pay
with this scenario? Will they get a refund? If so, how much?
d. Which option is better – marriage or not? Explain.
e. Would you consider this a marriage bonus or a marriage penalty? Why?
Wrap-up and look back:
19. Where else can someone making less than $100,000 in taxable income go to find their tax?
20. Describe the situation called “marriage bonus.”
Math 95 – Homework Unit 1 – Page 32
21. Describe the situation called “marriage penalty.”
22. When both people who are married earn about the same amount of money, is this an opportunity for a
marriage bonus or a marriage penalty? Explain.
23. When one person who is married earns significantly more than the other, is this an opportunity for a
marriage bonus or a marriage penalty? Explain.
24. Write in words what you learned from this section. Did you have any questions remaining that weren’t
covered in class? Write them out and bring them back to class.
1.10: Wrap-up and Review
1. In this list of formulas, can you see where to use each?
3.1: I  P  r  t and FV  P1  r  t 
3.2: FV  P1  i 
nt
1  i 
FV  pmt
nt
3.3:

1
i
3.4: P1  i   pmt
nt
3.5: UB  P1  i 
k
1  i 
nt

1
i
1  i   1
 pmt
3.6: P1  i nt  pmt
k
1  i 
nt
i
1

  1  c t
1 

 1 r 
3.7: P  pmt 
r c










3.8: a  b x  log b a  x  x 
loga 
logb 

P i 

log1 
pmt 

3.9: k  
log1  i 
i
2. Which type of account earns interest based on the principal investment only?
3. Find the amount of simple interest from the following:
a. A loan of $13,200 at 8.25% annual simple interest for 5 years.
b. A loan of $35,200 at 7.25% annual simple interest for 15 months.
c. An investment of $7,900 at 9.25% monthly simple interest for 15 years.
d. An investment of $900 at 6.25% monthly simple interest for 15 months.
e. An investment of $1,350 at 5.25% annual simple interest for 15 days.
4. Solve these simple interest problems for the missing piece.
a. Find the annual simple interest rate for a loan of 48 months with $2,350 interest on principal of
$32,000.
b. Find the principal needed to earn $2,711 in interest on 5% monthly simple interest over 6 years.
c. Find the principal needed to earn $397 in interest on 4.3% annual simple interest over 45 days.
d. Find the time needed to earn $700 in interest on an investment of $900 at 4.2% annual simple
interest.
5. What is the future value of …
a. $3,950 at 3% annual simple interest for 13 months?
b. $12,950 at 11.25% annual simple interest for 13 years?
Math 95 – Homework Unit 1 – Page 33
6. Determine the present value that will yield a future value of $39,400 at 6.25% annual simple interest for
2 years.
7. Determine the monthly payment and total interest paid for an add-on interest loans on a principal
amount of $58,000 at 3.75% annual simple interest for 7 years.
8. Determine the finance charge for the credit card based on an ADB of $1,386 at 24.99% annual simple
interest over June.
9. Determine (i) the finance charge, (ii) the new balance, and (iii) the minimum payment amount. Assume
the credit card requires 3% rounded up to nearest $5.
a. Peter has a credit card with an ADB of $6,694.78, with a remaining balance of $6,753.91. His
interest rate is 17.99% simple interest over December.
b. Ophelia has a credit card with an ADB of $1,984.28, with a remaining balance of $1,190.25. Her
interest rate is 12.99% simple interest over March.
10. Find the future value of $40,000 at 7% annual interest compounded monthly after: (a) 6 months, (b) 15
years, and (c) 30 years. Compare each with the value using 7% annual simple interest. Round to the
nearest penny at the end of the computations.
11. Determine the future value of $29,000 at 2.99% annual interest compounded weekly for 10 years, and
determine the amount of interest earned.
12. Determine the present value of $29,000 at 5% annual interest compounded daily for 13 years, and
determine the amount of interest earned.
13. Assume prices are rising at 7.92% each year. If the current cost of a car is $23,000, what will the price
of the car be in 25 years?
14. Determine which table would you use for the following problem? Then use the appropriate table to
determine the value.
a. If you invest $6,500 each year in an account earning 6% annual interest compounded annually, how
much would you have in 13 years?
b. If you invest $6,500 in an account earning 9% annual interest compounded annually, how much
would you have in 13 years?
15. Invest with Annuities a few more times.
a. If you invest $5,500 each year for a Roth IRA, and you do this for 26 years, how much will be in
the account if it earns 6.25% annual interest compounded annually. Figure out how much you paid
in and how much interest was earned.
b. If you invested $5,500 from age 30 to age 50, then invested $6,500 from age 50 to age 67,
determine how much money you would have in the account. Assume 6.25% annual interest
compounded annually. Determine how much you paid in and the amount of interest.
16. Work some annuities backwards – find the payment.
a. How much money do you need to invest each month at 5.75% annual interest compounded monthly
for 18 years to end with $48,000 (for your baby’s education)? Determine how much interest is
earned.
b. Because of extraordinary circumstances, your friend is now 55 years old and hasn’t started saving
for retirement yet. She wants to have $200,000 when she retires at age 70. How much should she
invest each month at 6.5% annual interest compounded monthly? Determine how much interest she
will earn.
Math 95 – Homework Unit 1 – Page 34
17. Use the formula to find the monthly payment and the amount of interest paid.
a. A mortgage of $325,000 at 4.15% annual interest compounded monthly for 30 years.
b. A student loan of $69,600 at 4.29% annual interest compounded monthly for 10 years.
18. Use the formula to determine the missing piece that will match the information given.
a. You can afford $287 per month for a car; determine how much of a loan amount you can afford for
4 years at 4.25% annual interest compounded monthly. Round loan amount down to the nearest
dollar.
b. If the car loan has a balance of $7,920 and the interest rate is 5.75% annual interest compounded
monthly, what is the amount needed to be paid each month to have this paid off in 3 years?
c. A credit card has a balance of $4,215 and your friend wants to pay it off over 3 years. The interest
rate is 16.49% annual interest compounded monthly – what monthly payment is needed?
19. True/False – explain your answer if you choose ‘False’:
a. Add-on interest loans charge interest on the principal only.
b. Amortized loans charge interest on the remaining balance.
c. Add-on interest loans have equal monthly payments.
d. The total interest paid on amortized loans is calculated with I  P  r  t .
e. The monthly interest paid on amortized loans is calculated with I  P  r  t .
f. Paying extra on amortized loans will save you time.
g. Paying extra on amortized loans will save you money.
h. Paying extra on add-on interest loans will save you time.
i. Paying extra on add-on interest loans will save you money.
20. Determine (i) the monthly P & I payment, (ii) the amount of interest paid in the first month, and (iii) the
amount of the P & I payment that goes to pay off the remaining balance.
a. A mortgage for $625,000 at 3.45% annual interest compounded monthly for 30 years.
b. A car loan for $11,900 at 7.25% annual interest compounded monthly for 3 years.
21. Jackie is considering two mortgages on her loan amount of $373,500. The first is a 30 year mortgage at
4.45% annual interest compounded monthly and the second is a 15 year mortgage at 3.89% annual
interest compounded monthly. Compare these options and determine which is best for her:
a. She takes the 30 year option and makes the 30 year P & I payment for 30 years.
b. She takes the 15 year option and makes the 15 year P & I payment for 15 years.
c.
She takes the 30 year option and makes the 15 year P & I payment until paid off.
22. Consider the problem above with Jackie – she takes the 30 year loan and makes payments of $3,700 for
4 years. Approximate her unpaid balance.
Math 95 – Homework Unit 1 – Page 35
23. Mitchell knows that he needs $4,300 per month to live comfortably now. He plans to retire in about 31
years and plans to be retired for about 24 years after that. Determine…
a. how much he needs each month to maintain his current standard of living when he retires 31 years
from now (assuming 2.8% inflation).
b. how much he needs to have in his retirement account to be paid out equal monthly amounts of the
amount in (a) each month for 24 years if the account earns 5.4% annual interest compounded
monthly.
c. how much he needs to invest each month at 8.25% annual interest compounded monthly over the
next 31 years in order to have the amount in (b).
d. how much interest he earned over the course of the 55 years.
24. Peeta knows that he needs $4,300 per month to live comfortably now. He plans to retire in about 31
years and plans to be retired for about 24 years after that. Determine…
a. how much he needs each month to maintain his current standard of living when he retires 31 years
from now (assuming 2.8% inflation).
b. how much he needs to have in his retirement account to be paid out using a COLA payout annuity
with annual payments equivalent to the amount from (a) multiplied by 12. He wants payments to
increase by 2.8% each year for 24 years if the account earns 5.4% annual interest compounded
monthly.
c. how much he needs to invest each month at 8.25% annual interest compounded monthly over the
next 31 years in order to have the amount in (b).
d. how much interest he earned over the course of the 55 years.
e. Compare this COLA option with the fixed payment option.
25. If the first payment from a COLA payout annuity is $49,000, and the COLA is 3.1%, determine…
a. The amount of the 2nd payment.
b. The amount of the 10th payment.
c. The amount of the 24th payment.
d. The amount of the 31st payment.
26. In order to determine the total amount paid out from a COLA payout annuity, we can use a formula
1  i   1 . When using this formula, the pmt is the first payment made
we’ve seen before: FV  pmt
nt
i
and the periodic rate is computed using the COLA rate, not the interest rate. The future value will be
the sum of all the payments! Determine the amount paid out of these COLA payout annuities:
a. First payment of $69,500 with cost of living as 2.7% and interest of 4.75% annual interest
compounded annually, over 20 years.
b. First payment of $163,500 with cost of living as 3.1% and interest of 6.75% annual interest
compounded annually, over 13 years.
c. First payment of $163,500 with cost of living as 3.1% and interest of 2.75% annual interest
compounded annually, over 13 years.
Math 95 – Homework Unit 1 – Page 36
27. Solve the following equations using your calculator. If the answer is not exact, round to 4 decimal
places. Be sure to check your work with each one.
a. 7 n  243
n
b. 1,1001.0525  12,000
c.
d.
1.0325n  3.21
n
60.8  4
28. Determine how long it would take for the present value to become the future value.
a. How long until $50,000 becomes $120,000 at 4.5% annual interest compounded monthly?
b. How long to turn $5,400 into $25,000 if the rate is 6.5% annual interest compounded monthly?

P i 

log1 
pmt 

29. Use the formula k  
to see how long it would take to pay off the given debts.
log1  i 
a. How long would it take to pay off a student loan of $28,000 if you can afford monthly payments of
$210 and the interest rate is 4.89% annual interest compounded monthly?
b. How long would it take to pay off a mortgage of $311,000 if you can suddenly afford monthly
payments of $2,900 and the interest rate is 3.23% annual interest compounded monthly?
30. Jon Snow is filling out his taxes for 2015. He has income of $55,500 and is deciding whether or not to
get married during 2015. If so, he can claim MFJ status instead of single. His fiancée, Ygritte, has
income of $85,300 and has 1 child. She can claim the child tax credit of $1,000 for her child. Both will
take the standard deduction either way. The total amount withheld for federal taxes was $8,563 for him
and $9,112 for her.
a. Consider Jon filing as single and not getting married in 2015. How much tax will he pay with this
scenario? Will he get a refund? If so, how much?
b. Consider Ygritte filing as HoH and not getting married in 2015. How much tax will she pay with
this scenario? Will she get a refund? If so, how much?
c. Consider the two getting married at the end of 2015 and filing as MFJ. How much tax will they pay
with this scenario? Will they get a refund? If so, how much?
d. Which option is better – marriage or not? Explain.
e. Would you consider this a marriage bonus or a marriage penalty? Why?
Math 95 – Homework Unit 1 – Page 37