ch5
Student: _______________________________________________________________________________________
Multiple Choice Questions
1. The amount an investment will be worth after one or more periods of time is the _____ value.
A.
B.
C.
D.
E.
future
present
principal
discounted
simple
2. The process of accumulating interest on an investment over time to earn more interest is called:
A.
B.
C.
D.
E.
growth.
compounding.
aggregation.
accumulation.
discounting.
3. Interest earned on the reinvestment of previous interest payments is called _____ interest.
A.
B.
C.
D.
E.
free
annual
simple
interest on
compound
4. Interest earned on both the initial principal and the interest reinvested from prior periods is called
_____ interest.
A.
B.
C.
D.
E.
free
annual
simple
interest on
compound
5. Interest earned only on the original principal amount invested is called _____ interest.
A.
B.
C.
D.
E.
free
annual
simple
interest on
compound
6. The future value interest factor is computed as:
A. (1 + r)t.
B. (1 + rt).
C. (1 + r) t.
D. 1 + r t.
E. (1+ r)
rt.
7. The value today of future cash flows discounted at the appropriate discount rate is called the _____
value.
A.
B.
C.
D.
E.
principal
future
present
simple
compound
8. The process of finding the present value of some future amount is commonly called:
A.
B.
C.
D.
E.
growth.
discounting.
accumulation.
compounding.
reduction.
9. The present value interest factor is computed as:
A. 1 / (1 + r t).
B. 1 / (1 + rt).
C. 1 / (1 + r) t.
D. 1 / (1 + r)t.
E. 1 + r + t.
10. The interest rate used to calculate the present value of future cash flows is called the _____ rate.
A.
B.
C.
D.
E.
free
annual
compound
simple
discount
11. As the discount rate increases, the present value of $2,000 to be received four years from now:
A.
B.
C.
D.
E.
remains constant.
also increases.
decreases.
becomes negative.
will vary but the direction of the change is unknown.
12. Jeff is going to receive $10,000 five years from now. Tammy is going to receive $10,000 eight years
from now. Which one of the following statements is correct if both Tammy and Jeff apply a 6
percent discount rate to these amounts?
A.
B.
C.
D.
E.
The present value of Tammy's and Jeff's money will be equal.
The value of Jeff's money will be less than the value of Tammy's money 15 years from now.
In today's dollars, Jeff's money is worth more than Tammy's.
Ten years from now, the value of Jeff's money will be equal to the value of Tammy's money.
Tammy's money is worth more than Jeff's money given the 6 percent discount rate.
13. Tracie deposits $5,000 into an account that pays 3 percent interest compounded annually. Chris
deposits $5,000 into an account that pays 3 percent simple interest. Both deposits were made this
morning. Which of the following statements are true concerning these two accounts?
I. At the end of one year, both Tracie and Chris will have the same amount in their accounts.
II. At the end of five years, Tracie will have more money in her account than Chris has in his.
III. Chris will never earn any interest on interest.
IV. All else equal, Chris made the better investment.
A.
B.
C.
D.
E.
I and II only
III and IV only
I, II, and III only
I, III, and IV only
II, III, and IV only
14. Kate invests $3,000 at 9 percent when she is 20 years old. Kurt invests $3,000 at 9 percent when he
is 35 years old. Both investments compound interest annually. Both Kate and Kurt retire at age 60.
Which one of the following statements is correct?
A.
B.
C.
D.
E.
Kate will have less money when she retires than Kurt.
Kurt will earn more interest on interest than Kate.
Kurt will earn more compound interest than Kate.
If Kurt waits to age 70 to retire, then he will have just as much money as Kate.
Kate will have more money when she retires than Kurt.
15. Raoul has $800 today. Which one of the following statements is correct if he invests this money at a
positive rate of interest for ten years? Assume the interest is compounded annually.
A.
B.
C.
D.
The higher the interest rate he earns, the less money he will have in the future.
The higher the interest rate, the longer he has to wait for his money to grow to $2,000 in value.
If Raoul can earn 7 percent, he will have to wait about six years to have $1,600 total.
At the end of the ten years, Raoul will have less money if he invests at 9 percent rather than at 8
percent.
E. At 7.2 percent interest, Raoul should expect to have about $1,600 in his account at the end of the ten
years.
16. Frank invests $2,500 in an account that pays 6 percent simple interest. How much money will he
have at the end of four years?
A. $2,650
B. $3,100
C. $3,156
D. $3,163
E. $10,600
17. Faith invests $4,500 in an account that pays 4 percent simple interest. How much money will she
have at the end of eight years?
A.
B.
C.
D.
E.
$4,680
$5,367
$5,940
$6,122
$6,159
18. Jessica invests $3,000 in an account that pays 5 percent simple interest. How much more could she
have earned over a 7-year period if the interest had compounded annually?
A.
B.
C.
D.
E.
$122.20
$129.20
$147.80
$171.30
$221.30
19. Jeff invests $3,000 in an account that pays 7 percent simple interest. How much more could he have
earned over a 20-year period if the interest had compounded annually?
A.
B.
C.
D.
E.
$2,840.00
$3,212.12
$3,778.54
$4,087.18
$4,409.05
20. What is the future value of $3,497 invested for 15 years at 7.5 percent compounded annually?
A.
B.
C.
D.
E.
$7,431.13
$10,347.19
$14,289.16
$14,911.08
$15,267.21
21. Today, you earn a salary of $42,500. What will be your annual salary 10 years from now if you earn
annual raises of 3.2 percent?
A.
B.
C.
D.
E.
$56,100.00
$57,414.06
$58,235.24
$59,122.08
$59,360.45
22. You own a classic automobile that is currently valued at $67,900. If the value increases by 8 percent
annually, how much will the automobile be worth 15 years from now?
A.
B.
C.
D.
E.
$199,801.33
$212,524.67
$214,740.01
$215,390.28
$218,887.79
23. You hope to buy your dream house 3 years from now. Today, your dream house costs $247,900.
You expect housing prices to rise by an average of 7.5 percent per year over the next 3 years. How
much will your dream house cost by the time you are ready to buy it?
A.
B.
C.
D.
E.
$292,063.48
$294,882.01
$298,600.00
$307,965.40
$309,425.45
24. Your grandmother invested one lump sum 42 years ago at 3.5 percent interest. Today, she gave you
the proceeds of that investment which totaled $28,204.37. How much did your grandmother
originally invest?
A.
B.
C.
D.
E.
$4,500
$6,650
$7,200
$7,500
$9,000
25. What is the present value of $36,800 to be received 6 years from today if the discount rate is 12
percent?
A.
B.
C.
D.
E.
$18,644.03
$19,407.18
$19,414.14
$20,211.08
$20,390.14
26. You would like to give your daughter $50,000 towards her college education 15 years from now.
How much money must you set aside today for this purpose if you can earn 9 percent on your
investments?
A.
B.
C.
D.
E.
$12,250.00
$12,989.47
$13,726.90
$14,008.50
$14,211.11
27. One year ago, you invested $2,500. Today it is worth $2,789.50. What rate of interest did you earn?
A. 8.67 percent
B. 9.89 percent
C. 10.67 percent
D. 11.42 percent
E. 11.58 percent
28. Thirty years ago, your father invested $11,000. Today, that investment is worth $287,047. What is
the average annual rate of return your father earned on his investment?
A.
B.
C.
D.
E.
11.14 percent
11.27 percent
11.38 percent
11.49 percent
12.07 percent
29. Twelve years ago, Jake invested $2,000. Six years ago, Tami invested $4,000. Today, both Jake's
and Tami's investments are each worth $9,700. Assume that both Jake and Tami continue to earn
their respective rates of return. Which one of the following statements is correct concerning these
investments?
A.
B.
C.
D.
E.
Three years from today, Jake's investment will be worth more than Tami's.
One year ago, Tami's investment was worth more than Jake's.
Jake has earned a higher rate of return than Tami.
Tami has earned an average annual interest rate of 15.91 percent.
Jake has earned an average annual interest rate of 15.47 percent.
30. Tropical Tans is saving money to build a new salon. Three years ago, they set aside $12,000 for this
purpose. Today, that account is worth $16,418. What rate of interest is Tropical Tans earning on this
money?
A.
B.
C.
D.
E.
10.88 percent
10.97 percent
11.01 percent
11.14 percent
11.23 percent
31. Five years ago, Precision Tool set aside $50,000 in case of a financial emergency. Today, that
account has increased in value to $64,397. What rate of interest is the firm earning on this money?
A.
B.
C.
D.
E.
5.19 percent
5.47 percent
6.18 percent
6.32 percent
6.45 percent
32. Six years ago, Home Health Industries (HHI) adopted a plan to expand its services next year. At the
time the plan was adopted, HHI set aside $125,000 in excess funds to be held for this purpose. As of
today, that money has increased in value to $186,408. What rate of interest is the firm earning on
these funds?
A. 6.89 percent
B. 7.10 percent
C. 7.18 percent
D. 7.27 percent
E. 7.43 percent
33. Some time ago, Richard purchased five acres of land costing $123,400. Today, that land is valued at
$189,700. How long has he owned this land if the price of land has been increasing at 5.5 percent
per year?
A.
B.
C.
D.
E.
6.01 years
6.98 years
7.42 years
8.03 years
8.67 years
34. On your thirteenth birthday, you received $1,000 which you invested at 6.5 percent interest,
compounded annually. Your investment is now worth $5,476. How old are you today?
A.
B.
C.
D.
E.
age 29
age 32
age 35
age 37
age 40
35. You want to have $260,000 saved 15 years from now. How much less do you have to deposit today
to reach this goal if you can earn 8 percent rather than 7 percent on your savings?
A.
B.
C.
D.
E.
$8,728.44
$12,273.13
$16,602.12
$17,414.41
$20,019.27
36. Your big brother deposited $10,000 today at 9 percent interest for 6 years. You would like to have
just as much money at the end of the next 6 years as your brother. However, you can only earn 7.5
percent interest. How much more money must you deposit today than your brother did if you are to
have the same amount at the end of the 6 years?
A.
B.
C.
D.
E.
$398.68
$487.63
$575.00
$648.21
$866.96
37. Last year, you deposited $25,000 into a retirement savings account at a fixed rate of 7.5 percent.
Today, you could earn a fixed rate of 8 percent on a similar type account. However, your rate is
fixed and cannot be adjusted. How much less could you have deposited last year if you could have
earned a fixed rate of 8 percent and still have the same amount as you currently will when you retire
40 years from today?
A. $1,218.46 less
B. $1,666.67 less
C. $2,408.28 less
D. $3,628.09 less
E. $4,331.30 less
38. When you retire 36 years from now, you want to have $2 million. You think you can earn an
average of 11.5 percent on your investments. To meet your goal, you are trying to decide whether to
deposit a lump sum today, or to wait and deposit a lump sum 3 years from today. How much more
will you have to deposit as a lump sum if you wait for 3 years before making the deposit?
A.
B.
C.
D.
E.
$15,344.14
$15,677.78
$16,208.11
$17,021.12
$19,407.78
39. Marie needs $26,000 as a down payment for a house 4 years from now. She earns 5.25 percent on
her savings. Marie can either deposit one lump sum today for this purpose or she can wait a year and
deposit a lump sum. How much additional money must Marie deposit if she waits for one year rather
than making the deposit today?
A.
B.
C.
D.
E.
$878.98
$911.13
$1,112.36
$1,348.03
$1,420.18
40. Wexter and Daughter invested $165,000 to help fund a company expansion project planned for 3
years from now. How much additional money will the firm have saved 3 years from now if it can
earn 7 percent rather than 5 percent on this money?
A.
B.
C.
D.
E.
$7,940.09
$8,218.07
$11,123.97
$12,648.18
$13,211.21
41. You just received $278,000 from an insurance settlement. You have decided to set this money aside
and invest it for your retirement. Currently, your goal is to retire 38 years from today. How much
more will you have in your account on the day you retire if you can earn an average return of 9.5
percent rather than just 9.0 percent?
A.
B.
C.
D.
E.
42.
$794,014
$1,396,036
$1,611,408
$1,818,342
$2,033,333
You will be receiving $2,500 from your family as a graduation present. You have decided to save
this money for your retirement. You plan to retire 40 years after graduation. How much additional
money will you have at that time if you can earn an average of 12.5 percent on your investment
instead of just 12 percent?
A.
B.
C.
D.
E.
$45,370.08
$51,400.62
$53,018.97
$58,811.99
$64,367.48
43. You deposit $1,000 in a retirement account today at 8.5 percent interest. How much more money
will you have if you leave the money invested for 40 years rather than 35 years?
A.
B.
C.
D.
E.
$7,714.91
$7,799.08
$7,839.73
$7,846.52
$8,753.38
44. You collect old model trains. One particular model increases in value at a rate of 6.5 percent per
year. Today, the model is worth $1,670. How much additional money can you make if you wait 4
years to sell the model rather than selling it 2 years from now?
A.
B.
C.
D.
E.
$196.67
$208.04
$241.79
$254.24
$280.15
Essay Questions
45. Write a sentence explaining why present values decrease as the discount rate increases.
46. Explain the relationship between compound interest and time.
47. Draw a graph illustrating the future value of $1, using five different interest rates (including 0
percent) and maturities ranging from today to 10 years from now. Plot time to maturity on the
horizontal axis and dollars on the vertical axis. (Note: You do not need to do any calculations. Just
draw the graph using your intuition.)
48. You are considering two lottery payment streams, choice A pays $1,000 today and choice B pays
$1,500 at the end of five years. Using a discount rate of 5 percent, based on present values, which
would you choose? Using the same discount rate of 5 percent, based on future values five years from
now, which would you choose? What do your results suggest as a general rule for approaching such
problems? (Make your choices based purely on the time value of money.)
49. At an interest rate of 10 percent and using the Rule of 72, how long will it take to double the value
of a lump sum invested today? How long will it take after that until the account grows to four times
the initial investment? Given the power of compounding, shouldn't it take less time for the money to
double the second time?
50. Some financial advisors recommend you increase the amount of federal income taxes withheld from
your paycheck each month so that you will get a larger refund come April 15th. That is, you take
home less today but get a bigger lump sum when you get your refund. Based on your knowledge of
the time value of money, what do you think of this idea? Explain.
ch5 KEY
Multiple Choice Questions
1. The amount an investment will be worth after one or more periods of time is the _____ value.
A.
B.
C.
D.
E.
future
present
principal
discounted
simple
Ross - Chapter 005 #1
SECTION: 5.1
TOPIC: FUTURE VALUE
TYPE: DEFINITIONS
2. The process of accumulating interest on an investment over time to earn more interest is called:
A.
B.
C.
D.
E.
growth.
compounding.
aggregation.
accumulation.
discounting.
Ross - Chapter 005 #2
SECTION: 5.1
TOPIC: COMPOUNDING
TYPE: DEFINITIONS
3. Interest earned on the reinvestment of previous interest payments is called _____ interest.
A.
B.
C.
D.
E.
free
annual
simple
interest on
compound
Ross - Chapter 005 #3
SECTION: 5.1
TOPIC: INTEREST ON INTEREST
TYPE: DEFINITIONS
4. Interest earned on both the initial principal and the interest reinvested from prior periods is called
_____ interest.
A.
B.
C.
D.
E.
free
annual
simple
interest on
compound
Ross - Chapter 005 #4
SECTION: 5.1
TOPIC: COMPOUND INTEREST
TYPE: DEFINITIONS
5. Interest earned only on the original principal amount invested is called _____ interest.
A.
B.
C.
D.
E.
free
annual
simple
interest on
compound
Ross - Chapter 005 #5
SECTION: 5.1
TOPIC: SIMPLE INTEREST
TYPE: DEFINITIONS
6. The future value interest factor is computed as:
A. (1 + r)t.
B. (1 + rt).
C. (1 + r) t.
D. 1 + r t.
E. (1+ r)
rt.
Ross - Chapter 005 #6
SECTION: 5.1
TOPIC: FUTURE VALUE INTEREST FACTOR
TYPE: DEFINITIONS
7. The value today of future cash flows discounted at the appropriate discount rate is called the _____
value.
A.
B.
C.
D.
E.
principal
future
present
simple
compound
Ross - Chapter 005 #7
SECTION: 5.2
TOPIC: PRESENT VALUE
TYPE: DEFINITIONS
8. The process of finding the present value of some future amount is commonly called:
A.
B.
C.
D.
E.
growth.
discounting.
accumulation.
compounding.
reduction.
Ross - Chapter 005 #8
SECTION: 5.2
TOPIC: DISCOUNTING
TYPE: DEFINITIONS
9. The present value interest factor is computed as:
A. 1 / (1 + r t).
B. 1 / (1 + rt).
C. 1 / (1 + r) t.
D. 1 / (1 + r)t.
E. 1 + r + t.
Ross - Chapter 005 #9
SECTION: 5.2
TOPIC: PRESENT VALUE INTEREST FACTOR
TYPE: DEFINITIONS
10. The interest rate used to calculate the present value of future cash flows is called the _____ rate.
A.
B.
C.
D.
E.
free
annual
compound
simple
discount
Ross - Chapter 005 #10
SECTION: 5.2
TOPIC: DISCOUNT RATE
TYPE: DEFINITIONS
11. As the discount rate increases, the present value of $2,000 to be received four years from now:
A.
B.
C.
D.
E.
remains constant.
also increases.
decreases.
becomes negative.
will vary but the direction of the change is unknown.
Ross - Chapter 005 #11
SECTION: 5.2
TOPIC: PRESENT VALUE AND DISCOUNT RATE
TYPE: CONCEPTS
12. Jeff is going to receive $10,000 five years from now. Tammy is going to receive $10,000 eight years
from now. Which one of the following statements is correct if both Tammy and Jeff apply a 6
percent discount rate to these amounts?
A.
B.
C.
D.
E.
The present value of Tammy's and Jeff's money will be equal.
The value of Jeff's money will be less than the value of Tammy's money 15 years from now.
In today's dollars, Jeff's money is worth more than Tammy's.
Ten years from now, the value of Jeff's money will be equal to the value of Tammy's money.
Tammy's money is worth more than Jeff's money given the 6 percent discount rate.
Ross - Chapter 005 #12
SECTION: 5.2
TOPIC: PRESENT VALUE AND TIME
TYPE: CONCEPTS
13. Tracie deposits $5,000 into an account that pays 3 percent interest compounded annually. Chris
deposits $5,000 into an account that pays 3 percent simple interest. Both deposits were made this
morning. Which of the following statements are true concerning these two accounts?
I. At the end of one year, both Tracie and Chris will have the same amount in their accounts.
II. At the end of five years, Tracie will have more money in her account than Chris has in his.
III. Chris will never earn any interest on interest.
IV. All else equal, Chris made the better investment.
A.
B.
C.
D.
E.
I and II only
III and IV only
I, II, and III only
I, III, and IV only
II, III, and IV only
Ross - Chapter 005 #13
SECTION: 5.1
TOPIC: SIMPLE VERSUS COMPOUND INTEREST
TYPE: CONCEPTS
14. Kate invests $3,000 at 9 percent when she is 20 years old. Kurt invests $3,000 at 9 percent when he
is 35 years old. Both investments compound interest annually. Both Kate and Kurt retire at age 60.
Which one of the following statements is correct?
A.
B.
C.
D.
E.
Kate will have less money when she retires than Kurt.
Kurt will earn more interest on interest than Kate.
Kurt will earn more compound interest than Kate.
If Kurt waits to age 70 to retire, then he will have just as much money as Kate.
Kate will have more money when she retires than Kurt.
Ross - Chapter 005 #14
SECTION: 5.1
TOPIC: FUTURE VALUE AND TIME
TYPE: CONCEPTS
15. Raoul has $800 today. Which one of the following statements is correct if he invests this money at a
positive rate of interest for ten years? Assume the interest is compounded annually.
A.
B.
C.
D.
The higher the interest rate he earns, the less money he will have in the future.
The higher the interest rate, the longer he has to wait for his money to grow to $2,000 in value.
If Raoul can earn 7 percent, he will have to wait about six years to have $1,600 total.
At the end of the ten years, Raoul will have less money if he invests at 9 percent rather than at 8
percent.
E. At 7.2 percent interest, Raoul should expect to have about $1,600 in his account at the end of the ten
years.
Ross - Chapter 005 #15
SECTION: 5.1
TOPIC: RULE OF 72
TYPE: CONCEPTS
16. Frank invests $2,500 in an account that pays 6 percent simple interest. How much money will he
have at the end of four years?
A.
B.
C.
D.
E.
$2,650
$3,100
$3,156
$3,163
$10,600
Ending value = $2,500 + ($2,500
.06
4) = $3,100.00
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #16
SECTION: 5.1
TOPIC: SIMPLE INTEREST
TYPE: PROBLEMS
17. Faith invests $4,500 in an account that pays 4 percent simple interest. How much money will she
have at the end of eight years?
A.
B.
C.
D.
E.
$4,680
$5,367
$5,940
$6,122
$6,159
Ending value = $4,500 + ($4,500
.04
8) = $5,940.00
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #17
SECTION: 5.1
TOPIC: SIMPLE INTEREST
TYPE: PROBLEMS
18. Jessica invests $3,000 in an account that pays 5 percent simple interest. How much more could she
have earned over a 7-year period if the interest had compounded annually?
A.
B.
C.
D.
E.
$122.20
$129.20
$147.80
$171.30
$221.30
Ending value at 5 percent simple interest = $3,000 + ($3,000
Ending value at 5 percent compounded annually = $3,000
Difference = $4,221.30
.05
7) = $4,050.00;
7
(1 + .05) = $4,221.30;
$4,050.00 = $171.30
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #18
SECTION: 5.1
TOPIC: SIMPLE VERSUS COMPOUND INTEREST
TYPE: PROBLEMS
19. Jeff invests $3,000 in an account that pays 7 percent simple interest. How much more could he have
earned over a 20-year period if the interest had compounded annually?
A.
B.
C.
D.
$2,840.00
$3,212.12
$3,778.54
$4,087.18
E. $4,409.05
Ending value at 7 percent simple interest = $3,000 + ($3,000
Ending value at 7 percent compounded annually = $3,000
Difference = $11,609.05
.07
20) = $7,200.00;
20
(1 + .07)
= $11,609.05;
$7,200.00 = $4,409.05
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #19
SECTION: 5.1
TOPIC: SIMPLE VERSUS COMPOUND INTEREST
TYPE: PROBLEMS
20. What is the future value of $3,497 invested for 15 years at 7.5 percent compounded annually?
A.
B.
C.
D.
E.
$7,431.13
$10,347.19
$14,289.16
$14,911.08
$15,267.21
Future value = $3,497
(1 + .075)
15
= $10,347.19
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #20
SECTION: 5.1
TOPIC: FUTURE VALUE
TYPE: PROBLEMS
21. Today, you earn a salary of $42,500. What will be your annual salary 10 years from now if you earn
annual raises of 3.2 percent?
A.
B.
C.
D.
E.
$56,100.00
$57,414.06
$58,235.24
$59,122.08
$59,360.45
Future value = $42,500
(1 + .032)
10
= $58,235.24
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #21
SECTION: 5.1
TOPIC: FUTURE VALUE
TYPE: PROBLEMS
22. You own a classic automobile that is currently valued at $67,900. If the value increases by 8 percent
annually, how much will the automobile be worth 15 years from now?
A.
B.
C.
D.
E.
$199,801.33
$212,524.67
$214,740.01
$215,390.28
$218,887.79
Future value = $67,900
(1 + .08)
15
= $215,390.28
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #22
SECTION: 5.1
TOPIC: FUTURE VALUE
TYPE: PROBLEMS
23. You hope to buy your dream house 3 years from now. Today, your dream house costs $247,900.
You expect housing prices to rise by an average of 7.5 percent per year over the next 3 years. How
much will your dream house cost by the time you are ready to buy it?
A.
B.
C.
D.
E.
$292,063.48
$294,882.01
$298,600.00
$307,965.40
$309,425.45
Future value = $247,900
3
(1 + .075) = $307,965.40
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #23
SECTION: 5.1
TOPIC: FUTURE VALUE
TYPE: PROBLEMS
24. Your grandmother invested one lump sum 42 years ago at 3.5 percent interest. Today, she gave you
the proceeds of that investment which totaled $28,204.37. How much did your grandmother
originally invest?
A.
B.
C.
D.
E.
$4,500
$6,650
$7,200
$7,500
$9,000
Present value = $28,204.37
42
[1 / (1 + .035) ] = $6,650.00
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #24
SECTION: 5.2
TOPIC: PRESENT VALUE
TYPE: PROBLEMS
25. What is the present value of $36,800 to be received 6 years from today if the discount rate is 12
percent?
A.
B.
C.
D.
E.
$18,644.03
$19,407.18
$19,414.14
$20,211.08
$20,390.14
Present value = $36,800
6
[1 / (1 + .12) ] = $18,644.03
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #25
SECTION: 5.2
TOPIC: PRESENT VALUE
TYPE: PROBLEMS
26. You would like to give your daughter $50,000 towards her college education 15 years from now.
How much money must you set aside today for this purpose if you can earn 9 percent on your
investments?
A.
B.
C.
D.
E.
$12,250.00
$12,989.47
$13,726.90
$14,008.50
$14,211.11
Present value = $50,000
15
[1 / (1 + .09) ] = $13,726.90
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #26
SECTION: 5.2
TOPIC: PRESENT VALUE
TYPE: PROBLEMS
27. One year ago, you invested $2,500. Today it is worth $2,789.50. What rate of interest did you earn?
A. 8.67 percent
B. 9.89 percent
C. 10.67 percent
D. 11.42 percent
E. 11.58 percent
$2,789.50 = $2,500
1
(1 + r) ; r = 11.58 percent
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #27
SECTION: 5.3
TOPIC: INTEREST RATE FOR A SINGLE PERIOD
TYPE: PROBLEMS
28. Thirty years ago, your father invested $11,000. Today, that investment is worth $287,047. What is
the average annual rate of return your father earned on his investment?
A.
B.
C.
D.
E.
11.14 percent
11.27 percent
11.38 percent
11.49 percent
12.07 percent
$287,047 = $11,000
30
(1 + r) ; r = 11.49 percent
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #28
SECTION: 5.3
TOPIC: INTEREST RATE FOR MULTIPLE PERIODS
TYPE: PROBLEMS
29. Twelve years ago, Jake invested $2,000. Six years ago, Tami invested $4,000. Today, both Jake's
and Tami's investments are each worth $9,700. Assume that both Jake and Tami continue to earn
their respective rates of return. Which one of the following statements is correct concerning these
investments?
A.
B.
C.
D.
E.
Three years from today, Jake's investment will be worth more than Tami's.
One year ago, Tami's investment was worth more than Jake's.
Jake has earned a higher rate of return than Tami.
Tami has earned an average annual interest rate of 15.91 percent.
Jake has earned an average annual interest rate of 15.47 percent.
12
Jake $9,700 = $2,000 (1 + r) ; r = 14.06 percent; Tami: $9,700 = $4,000
percent; The correct answer states that Tami earned 15.91 percent interest.
6
(1 + r) ; r = 15.91
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #29
SECTION: 5.3
TOPIC: INTEREST RATE FOR MULTIPLE PERIODS
TYPE: PROBLEMS
30. Tropical Tans is saving money to build a new salon. Three years ago, they set aside $12,000 for this
purpose. Today, that account is worth $16,418. What rate of interest is Tropical Tans earning on this
money?
A.
B.
C.
D.
E.
10.88 percent
10.97 percent
11.01 percent
11.14 percent
11.23 percent
$16,418 = $12,000
3
(1 + r) ; r = 11.01 percent
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #30
SECTION: 5.3
TOPIC: INTEREST RATE FOR MULTIPLE PERIODS
TYPE: PROBLEMS
31. Five years ago, Precision Tool set aside $50,000 in case of a financial emergency. Today, that
account has increased in value to $64,397. What rate of interest is the firm earning on this money?
A.
B.
C.
D.
E.
5.19 percent
5.47 percent
6.18 percent
6.32 percent
6.45 percent
$64,397 = $50,000
5
(1 + r) ; r = 5.19 percent
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #31
SECTION: 5.3
TOPIC: INTEREST RATE FOR MULTIPLE PERIODS
TYPE: PROBLEMS
32. Six years ago, Home Health Industries (HHI) adopted a plan to expand its services next year. At the
time the plan was adopted, HHI set aside $125,000 in excess funds to be held for this purpose. As of
today, that money has increased in value to $186,408. What rate of interest is the firm earning on
these funds?
A.
B.
C.
D.
E.
6.89 percent
7.10 percent
7.18 percent
7.27 percent
7.43 percent
$186,408 = $125,000
6
(1 + r) ; r = 6.89 percent
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #32
SECTION: 5.3
TOPIC: INTEREST RATE FOR MULTIPLE PERIODS
TYPE: PROBLEMS
33. Some time ago, Richard purchased five acres of land costing $123,400. Today, that land is valued at
$189,700. How long has he owned this land if the price of land has been increasing at 5.5 percent
per year?
A.
B.
C.
D.
E.
6.01 years
6.98 years
7.42 years
8.03 years
8.67 years
$189,700 = $123,400
t
(1 + .055) ; t = 8.03 years
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #33
SECTION: 5.3
TOPIC: NUMBER OF TIME PERIODS
TYPE: PROBLEMS
34. On your thirteenth birthday, you received $1,000 which you invested at 6.5 percent interest,
compounded annually. Your investment is now worth $5,476. How old are you today?
A.
B.
C.
D.
E.
age 29
age 32
age 35
age 37
age 40
$5,476 = $1,000
t
(1 + .065) ; t = 27 years; Age today = 13 + 27 = 40
Note: You received the money when you were 13 years old. Thus, you will be 40 (13 + 27) years old
when the value reaches $5,476.
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #34
SECTION: 5.3
TOPIC: NUMBER OF TIME PERIODS
TYPE: PROBLEMS
35. You want to have $260,000 saved 15 years from now. How much less do you have to deposit today
to reach this goal if you can earn 8 percent rather than 7 percent on your savings?
A.
B.
C.
D.
E.
$8,728.44
$12,273.13
$16,602.12
$17,414.41
$20,019.27
Present value = $260,000
15
[1 / (1 + .08) ] = $81,962.84; Present value = $260,000
= $94,235.97; Difference = $94,235.97
15
[1 / (1 + .07) ]
$81,962.84 = $12,273.13
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #35
SECTION: 5.2 AND 5.3
TOPIC: PRESENT VALUE AND RATE CHANGES
TYPE: PROBLEMS
36. Your big brother deposited $10,000 today at 9 percent interest for 6 years. You would like to have
just as much money at the end of the next 6 years as your brother. However, you can only earn 7.5
percent interest. How much more money must you deposit today than your brother did if you are to
have the same amount at the end of the 6 years?
A.
B.
C.
D.
E.
$398.68
$487.63
$575.00
$648.21
$866.96
Future value = $10,000
6
(1 + .09) = $16,771.00; Present value = $16,771.00
$10,866.96; Difference = $10,866.96
$10,000.00 = $866.96
6
[1 / (1 + .075) ] =
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #36
SECTION: 5.2 AND 5.3
TOPIC: PRESENT VALUE AND RATE CHANGES
TYPE: PROBLEMS
37. Last year, you deposited $25,000 into a retirement savings account at a fixed rate of 7.5 percent.
Today, you could earn a fixed rate of 8 percent on a similar type account. However, your rate is
fixed and cannot be adjusted. How much less could you have deposited last year if you could have
earned a fixed rate of 8 percent and still have the same amount as you currently will when you retire
40 years from today?
A.
B.
C.
D.
E.
$1,218.46 less
$1,666.67 less
$2,408.28 less
$3,628.09 less
$4,331.30 less
Future value = $25,000
(1 + .075)
41
= $484,938.92; Present value = $484,938.92
= $20,668.70; Difference = $25,000.00
[1
41
(1 + .08) ]
$20,668.70 = $4,331.30
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #37
SECTION: 5.2 AND 5.3
TOPIC: PRESENT VALUE AND TIME CHANGES
TYPE: PROBLEMS
38. When you retire 36 years from now, you want to have $2 million. You think you can earn an
average of 11.5 percent on your investments. To meet your goal, you are trying to decide whether to
deposit a lump sum today, or to wait and deposit a lump sum 3 years from today. How much more
will you have to deposit as a lump sum if you wait for 3 years before making the deposit?
A.
B.
C.
D.
E.
$15,344.14
$15,677.78
$16,208.11
$17,021.12
$19,407.78
Present value = $2,000,000
36
[1 / (1 + .115) ] = $39,731.48; Present value = $2,000,000
[1 / (1
33
+ .115) ] = $55,075.62; Difference = $55,075.62
$39,731.48 = $15,344.14
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #38
SECTION: 5.2 AND 5.3
TOPIC: PRESENT VALUE AND RATE CHANGES
TYPE: PROBLEMS
39. Marie needs $26,000 as a down payment for a house 4 years from now. She earns 5.25 percent on
her savings. Marie can either deposit one lump sum today for this purpose or she can wait a year and
deposit a lump sum. How much additional money must Marie deposit if she waits for one year rather
than making the deposit today?
A.
B.
C.
D.
E.
$878.98
$911.13
$1,112.36
$1,348.03
$1,420.18
Present value = $26,000
4
[1 / (1 + .0525) ] = $21,187.75; Present value = $26,000
= $22,300.11; Difference = $22,300.11
3
[1 / (1 + .0525) ]
$21,187.75 = $1,112.36
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #39
SECTION: 5.2 AND 5.3
TOPIC: PRESENT VALUE AND TIME CHANGES
TYPE: PROBLEMS
40. Wexter and Daughter invested $165,000 to help fund a company expansion project planned for 3
years from now. How much additional money will the firm have saved 3 years from now if it can
earn 7 percent rather than 5 percent on this money?
A.
B.
C.
D.
E.
$7,940.09
$8,218.07
$11,123.97
$12,648.18
$13,211.21
Future value = $165,000
3
(1 + .07) = $202,132.10; Future value = $165,000
3
(1 + .05) =
$191,008.13; Difference = $202,132.10
$191,008.13 = $11,123.97
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #40
SECTION: 5.1 AND 5.3
TOPIC: FUTURE VALUE AND RATE CHANGES
TYPE: PROBLEMS
41. You just received $278,000 from an insurance settlement. You have decided to set this money aside
and invest it for your retirement. Currently, your goal is to retire 38 years from today. How much
more will you have in your account on the day you retire if you can earn an average return of 9.5
percent rather than just 9.0 percent?
A.
B.
C.
D.
E.
$794,014
$1,396,036
$1,611,408
$1,818,342
$2,033,333
Future value = $278,000
(1 + .095)
38
= $8,745,433.15; Future value = $278,000
$7,349,397.17; Difference = $8,745,433.15
(1 + .09)
38
=
$7,349,397.17 = $1,396,036
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #41
SECTION: 5.1 AND 5.3
TOPIC: FUTURE VALUE AND RATE CHANGES
TYPE: PROBLEMS
42. You will be receiving $2,500 from your family as a graduation present. You have decided to save
this money for your retirement. You plan to retire 40 years after graduation. How much additional
money will you have at that time if you can earn an average of 12.5 percent on your investment
instead of just 12 percent?
A.
B.
C.
D.
E.
$45,370.08
$51,400.62
$53,018.97
$58,811.99
$64,367.48
Future value = $2,500
(1 + .125)
40
= $277,997.51; Future value = $2,500
$232,627.43; Difference = $277,997.51
(1 + .12)
40
=
$232,627.43 = $45,370.08
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #42
SECTION: 5.1 AND 5.3
TOPIC: FUTURE VALUE AND RATE CHANGES
TYPE: PROBLEMS
43. You deposit $1,000 in a retirement account today at 8.5 percent interest. How much more money
will you have if you leave the money invested for 40 years rather than 35 years?
A.
B.
C.
D.
E.
$7,714.91
$7,799.08
$7,839.73
$7,846.52
$8,753.38
Future value = $1,000
Difference = $26,133.02
(1 + .085)
40
= $26,133.02; Future value = $1,000
(1 + .085)
35
= $17,379.64;
$17,379.64 = $8,753.38
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #43
SECTION: 5.1 AND 5.3
TOPIC: FUTURE VALUE AND TIME CHANGES
TYPE: PROBLEMS
44. You collect old model trains. One particular model increases in value at a rate of 6.5 percent per
year. Today, the model is worth $1,670. How much additional money can you make if you wait 4
years to sell the model rather than selling it 2 years from now?
A.
B.
C.
D.
E.
$196.67
$208.04
$241.79
$254.24
$280.15
Future value = $1,670
4
(1 + .065) = $2,148.40; Future value = $1,670
2
(1 + .065) = $1,894.16;
Difference = $2,148.40
$1,894.16 = $254.24
AACSB TOPIC: ANALYTIC
Ross - Chapter 005 #44
SECTION: 5.1 AND 5.3
TOPIC: FUTURE VALUE AND TIME CHANGES
TYPE: PROBLEMS
Essay Questions
45. Write a sentence explaining why present values decrease as the discount rate increases.
Student answers will vary but should present the idea that when you can earn more interest, you need
less of your own money to reach the same future dollar amount.
AACSB TOPIC: REFLECTIVE THINKING
Ross - Chapter 005 #45
SECTION: 5.2
TOPIC: PRESENT VALUE AND DISCOUNTING
46. Explain the relationship between compound interest and time.
Interest compounds exponentially over time. The longer the time period, the greater the annual interest
earnings.
AACSB TOPIC: REFLECTIVE THINKING
Ross - Chapter 005 #46
SECTION: 5.1
TOPIC: COMPOUNDING
47. Draw a graph illustrating the future value of $1, using five different interest rates (including 0
percent) and maturities ranging from today to 10 years from now. Plot time to maturity on the
horizontal axis and dollars on the vertical axis. (Note: You do not need to do any calculations. Just
draw the graph using your intuition.)
Graphs should illustrate 3 concepts: 1) At zero percent interest, the $1 will not increase in value. 2) The
higher the interest rate, the higher the future value of $1. 3) The future values should illustrate
exponential growth.
AACSB TOPIC: REFLECTIVE THINKING
Ross - Chapter 005 #47
SECTION: 5.1
TOPIC: FUTURE VALUES
48. You are considering two lottery payment streams, choice A pays $1,000 today and choice B pays
$1,500 at the end of five years. Using a discount rate of 5 percent, based on present values, which
would you choose? Using the same discount rate of 5 percent, based on future values five years from
now, which would you choose? What do your results suggest as a general rule for approaching such
problems? (Make your choices based purely on the time value of money.)
PV of A = $1,000; PV of B = $1,175; FV of A = $1,276; FV of B = $1,500. Based on both present
values and future values, B is the better choice. The student should recognize that finding present values
and finding future values are simply reverse processes of one another, and that choosing between two
lump sums based on PV will always give the same result as choosing between the same two lump sums
based on FV.
AACSB TOPIC: REFLECTIVE THINKING
Ross - Chapter 005 #48
SECTION: 5.1 AND 5.2
TOPIC: COMPARING LUMP SUMS
49. At an interest rate of 10 percent and using the Rule of 72, how long will it take to double the value
of a lump sum invested today? How long will it take after that until the account grows to four times
the initial investment? Given the power of compounding, shouldn't it take less time for the money to
double the second time?
It will take 7.2 years to double the initial investment, then another 7.2 years to double it again. That is, it
takes 14.4 years for the value to reach four times the initial investment. Compounding doesn't affect the
amount of time it takes for an investment to double the second time, but note that during the first 7.2
years, the interest earned is equal to 100 percent of the initial investment. During the second 7.2 years,
the interest earned is equal to 200 percent of the initial investment. That is the power of compounding.
AACSB TOPIC: REFLECTIVE THINKING
Ross - Chapter 005 #49
SECTION: 5.3
TOPIC: RULE OF 72 AND COMPOUNDING
50. Some financial advisors recommend you increase the amount of federal income taxes withheld from
your paycheck each month so that you will get a larger refund come April 15th. That is, you take
home less today but get a bigger lump sum when you get your refund. Based on your knowledge of
the time value of money, what do you think of this idea? Explain.
Some students may slip in a discussion about the benefits of forced savings, etc., but these issues are
based on preferences, not the time value of money. Based on the time value of money, the student
should recommend just the opposite. That is, withhold as little as possible, while still avoiding tax
penalties for under withholding, and pay the remaining tax bill when it comes due the following year as
next year's dollars are cheaper than this year's dollars.
AACSB TOPIC: REFLECTIVE THINKING
Ross - Chapter 005 #50
SECTION: 5.3
TOPIC: THE TIME VALUE OF MONEY
ch5 Summary
Category
# of Questions
AACSB TOPIC: ANALYTIC
AACSB TOPIC: REFLECTIVE THINKING
Ross - Chapter 005
SECTION: 5.1
SECTION: 5.1 AND 5.2
SECTION: 5.1 AND 5.3
SECTION: 5.2
SECTION: 5.2 AND 5.3
SECTION: 5.3
TOPIC: COMPARING LUMP SUMS
TOPIC: COMPOUND INTEREST
TOPIC: COMPOUNDING
TOPIC: DISCOUNT RATE
TOPIC: DISCOUNTING
TOPIC: FUTURE VALUE
TOPIC: FUTURE VALUE AND RATE CHANGES
TOPIC: FUTURE VALUE AND TIME
TOPIC: FUTURE VALUE AND TIME CHANGES
TOPIC: FUTURE VALUE INTEREST FACTOR
TOPIC: FUTURE VALUES
TOPIC: INTEREST ON INTEREST
TOPIC: INTEREST RATE FOR A SINGLE PERIOD
TOPIC: INTEREST RATE FOR MULTIPLE PERIODS
TOPIC: NUMBER OF TIME PERIODS
TOPIC: PRESENT VALUE
TOPIC: PRESENT VALUE AND DISCOUNT RATE
TOPIC: PRESENT VALUE AND DISCOUNTING
TOPIC: PRESENT VALUE AND RATE CHANGES
TOPIC: PRESENT VALUE AND TIME
TOPIC: PRESENT VALUE AND TIME CHANGES
TOPIC: PRESENT VALUE INTEREST FACTOR
TOPIC: RULE OF 72
TOPIC: RULE OF 72 AND COMPOUNDING
TOPIC: SIMPLE INTEREST
TOPIC: SIMPLE VERSUS COMPOUND INTEREST
TOPIC: THE TIME VALUE OF MONEY
TYPE: CONCEPTS
TYPE: DEFINITIONS
TYPE: PROBLEMS
29
6
50
19
1
5
10
5
10
1
1
2
1
1
5
3
1
2
1
1
1
1
5
2
4
1
1
3
1
2
1
1
1
3
3
1
5
10
29