Test 2
Version B KEY
MATH 1010
Essential Mathematics
Spring 2016
Sections 3D – 5A
Formulas
Index number =
compared value
×100
reference value
 CPI y 
Price in $y = (price in $x) × 

 CPI x 
Rate of inflation =
or
CPI y
CPI x
=
Price in $ y
Price in $ x
CPINew − CPIOld
×100%
CPIOld
CPI: The Consumer
Year
1990
1991
1992
1993
1994
1995
1996
1997
Price Index (Source: US Bureau of Labor Statistics)
CPI
Year
CPI
130.7
1998
163.0
136.2
1999
166.6
140.3
2000
172.2
144.5
2001
177.1
148.2
2002
179.9
152.4
2003
184.0
156.9
2004
188.9
160.5
2005
195.3
Version B KEY – Page 1 of 17
Test 2
Version B KEY
MATH 1010
Essential Mathematics
Spring 2016
Sections 3D – 5A
A = P + (P × APR × Y)
APR 

A = P 1 +

n 

(nY )
P=
A = Pe( APR × Y )
APY = Total Return =
P=
A
APR 

1 +

n 

e
(nY )
A
( APR × Y )
A-P
× 100%
P
(nY )


APR 
−1 
  1 +


n 
  

A = PMT 

 APR 






 n 


PMT =
A
(nY )


APR 
−1 
  1 +


n 
  



 APR 




 n 




1


 
 A  Y  

Annual Return =   − 1 × 100%
 P 



 APR 
P

 n 
PMT =
( −nY ) 
 
APR 
1 −  1 +


n 
 

( − nY ) 
 
APR 
PMT 1 −  1 +


n 
 


P=
 APR 


 n 
Version B KEY – Page 2 of 17
Test 2
Version B KEY
MATH 1010
Essential Mathematics
Spring 2016
Sections 3D – 5A
Gross Income = Sum of All Income
Adjusted Gross Income = Gross Income – Adjustments to Income
Taxable Income = Adjusted Gross Income – (Deductions and Exemptions)
Total Income Tax = Tax Calculated from Table – Tax Credits
FICA Tax = 7.65% of Wages
Overall Federal Tax Rate =
Total Income Tax + FICA Tax
× 100%
Gross Income
2013 Marginal Tax Rates: Standard Deductions and Exemptions
Tax rate
Single
Married filing
Married filing
Head of
jointly
separately
household
10%
Up to $8,925
Up to $17,850
Up to $87,850
Up to $146,400
Up to $398,350
Up to $398,350
15%
Up to $36,250
28%
Up to $183,250
Deduct
$6,100
25%
33%
Exempt
$3,900
Margin of Error Estimate =
Up to $8,925
Up to $12,750
Up to $73,200
Up to $125,450
Up to $199,175
Up to $398,350
Up to $72,500
Up to $36,250
Up to $223,050
Up to $111,525
$12,200
$6,100
$3,900
$3,900
Up to $48,600
Up to $203,150
$8,950
$3,900
1
×100%
n
Version B KEY – Page 3 of 17
MATH 1010
Essential Mathematics
Test 2
Version B KEY
Spring 2016
Sections 3D – 5A
BLANK so that you may tear off the formula sheets.
Feel free to use this as scratch paper.
Version B KEY – Page 4 of 17
Test 2
Version B KEY
MATH 1010
Essential Mathematics
Spring 2016
Sections 3D – 5A
Student’s Printed Name: _____________________ XID: C___________
Instructor: _________________________________ Section: _________
No questions will be answered during this exam.
If you consider a question to be ambiguous, state your assumptions in the margin
and do the best you can to provide the correct answer.
You have 90 minutes (1.5 hours) to complete this test.
General Directions:
•
Any communication with any person (other than the instructor or a designated
proctor) during this exam of any form, including written, signed, verbal, or digital,
is understood to be a violation of academic integrity.
•
All devices, such as computers, cell phones, cameras, and PDAs, must be
turned off while the student is in the testing room.
•
You may use any scientific calculator except a TI-89 or a TI-NSpire CAS.
•
No part of this test may be removed from the examination room.
On my honor, I have neither given nor received inappropriate or unauthorized
information at any time before or during this test.
Student’s Signature:________________________________________________
Do not write below this line.
Question
1
2
3
4
Scantron
Points
7
11
9
12
1
Earned
Free Response Total
40
Multiple Choice Total
60
Test Score
Version B KEY – Page 5 of 17
MATH 1010
Essential Mathematics
Test 2
Version B KEY
Spring 2016
Sections 3D – 5A
Multiple Choice Portion
There are 20 multiple choice questions. Each question is worth 3 points and has one
correct answer. Use a number 2 pencil and bubble in the letter of your response on the
Scantron sheet. For your own record, also circle your choice on your test since the
Scantron will not be returned to you. Only the responses recorded on your Scantron
sheet will be graded.
1.
Suppose your filing status is Single (no dependents) and your gross income is
$46,000. You contributed $2,400 to a tax-deferred retirement plan. Assuming you
claim the standard deduction, what is your taxable income? Use the 2013 Tax Table.
A) $36,000
B) $38,400
C) $37,500
D) $33,600
E) $39,700
2.
Luke’s filing status is Single. He earned $62,000 in wages, $1,000 in interest, and
$4,570 in stock dividends. He contributed $3,350 to a tax-deferred retirement plan.
Find his Adjusted Gross Income (AGI).
A) $64,220
B) $62,000
C) $70,920
D) $63,000
E) $67,570
Version B KEY – Page 6 of 17
MATH 1010
Essential Mathematics
3.
Test 2
Version B KEY
Spring 2016
Sections 3D – 5A
A veterinarian conducted a test to see if cats dislike getting wet. The veterinarian
created a sample set consisting of cats from each of the 73 breeds recognized by
the International Progressive Cat Breeders Alliance (IPCBA). This sampling method
is best described as:
A) Total Sampling
B) Simple Random Sampling
C) Stratified Sampling
D) Systematic Sampling
E) Convenience Sampling
4.
Jane wants to buy a new car, but first she needs to save $12,500. If she has two
years to save in a 7.5% APR account compounded monthly, how much money
does she need to deposit each month? Round your answer to the nearest cent.
A) $67.63
B) $484.37
C) $25.81
D) $69,749.27
E) $237.86
5.
 APR 
P

 n 
In the formula PMT =
, what is the variable PMT?
( − nY ) 
 
APR 
1 −  1 +


n 
 

A) PMT is the monthly deposit into a savings plan.
B) PMT is the total of all payments made on a loan over Y years.
C) PMT is the amount of principal borrowed.
D) PMT is the monthly payment on a loan.
E) PMT is the amount in a savings plan at the end of Y years.
Version B KEY – Page 7 of 17
MATH 1010
Essential Mathematics
6.
Test 2
Version B KEY
Spring 2016
Sections 3D – 5A
A researcher wishes to determine the percentage of voters in a town who favor
stronger environmental laws. Which of the following would be the most
representative sample?
A) A sample of listeners who call in to a radio talk show
B) A sample selected randomly from the town’s phone book
C) A sample consisting of every 10th person leaving an organic food store
D) A random sample of college students
E) A stratified sample of the town’s doctors, lawyers, and politicians
7.
Jason bought a piano for $1,800. Eight years later, he sold it for $2,200. Calculate
the total return and annual return for this investment.
Round your answers to the nearest tenth of a percent.
A) Total Return = 22.2%; Annual Return = 2.8%
B) Total Return = –22.2%; Annual Return = –2.8%
C) Total Return = 22.2%; Annual Return = 2.5%
D) Total Return = 18.2%; Annual Return = 2.5%
E) Total Return = –18.2%; Annual Return = –2.5%
8.
David’s salary is $53,600. What is his FICA tax? Round your answer to the nearest cent.
A) $4,700.30
B) $3,618.00
C) $6,530.80
D) $4,100.40
E) $5,230.50
Version B KEY – Page 8 of 17
MATH 1010
Essential Mathematics
9.
Test 2
Version B KEY
Spring 2016
Sections 3D – 5A
A neurologist wanted to know the effect of long-term drug use on the brain. He
conducted a study by analyzing the brain scans of a group of people who were
long-term drug users and also of a group of people who had never used drugs.
What kind of study is this?
A) Double-blind
B) Single-blind
C) Experimental with no control group
D) Experimental
E) Case-controlled
10. Find the rate of inflation from 2004 to 2005.
Round your answer to the nearest tenth of a percent.
A) 3.3%
B) –6.4%
C) 6.4%
D) –3.3%
E) 3.4%
11. In November 2012, the average price of a loaf of whole wheat bread was $1.98.
Given CPI2012 is 229.6, estimate the price of a loaf of whole wheat bread in 1992.
Round your answer to two decimal places.
A) $1.57
B) $3.24
C) $1.21
D) $1.96
E) $2.21
Version B KEY – Page 9 of 17
MATH 1010
Essential Mathematics
Test 2
Version B KEY
Spring 2016
Sections 3D – 5A
12. Justine is making one initial deposit into a savings account that earns 3.35% APR
compounded quarterly. If she wants the account to have $20,000 in 18 years, how
much should she deposit now? Round your answer to the nearest cent.
A) $36,521.17
B) $12,476.61
C) $11,052.01
D) $19,342.00
E) $10,970.87
13. How much money would you have after 33 years and 9 months if you deposited
$560 in an account paying 4.35% APR compounded continuously?
Round your answer to the nearest cent.
A) $2,446.92
B) $1,382.15
C) $2,356.72
D) $2,431.01
E) $2,424.56
14. Based on the annual CPI, a yearly income of $25,000 in 1995 has the buying power
of what yearly income in 2005? Round your answer to the nearest thousand.
A) $32,000
B) $49,000
C) $20,000
D) $31,000
E) $38,000
Version B KEY – Page 10 of 17
MATH 1010
Essential Mathematics
Test 2
Version B KEY
Spring 2016
Sections 3D – 5A
15. Simon invests $4,500 in an account that pays 2.9% APR compounded monthly.
What is the APY of his account? Round the percentage to two decimal places.
A) 1.03%
B) 12.28%
C) 3.07%
D) 2.94%
E) 2.90%
16. Deb initially deposited $500 into an account with a simple interest rate of 1.5%.
Calculate the amount of money in Deb’s account at the end of 4 years.
Round your answer to the nearest cent.
A) $575.00
B) $531.00
C) $507.50
D) $800.00
E) $530.00
17. Using the Gasoline Price Index, calculate the price per gallon of gasoline in 2005.
Express your answer in cents/gallon rounded to one decimal place.
GPI-Gas: Gasoline Price Index (Source: US Department of Energy)
Price
Gasoline Price Index
Year
(cents/gallon)
1975 = 100
1975
56.7
100.
1985
119.6
210.9
1995
120.5
212.5
2005
??
407.4
A) 231.0 cents/gallon
B) 152.4 cents/gallon
C) 174.3 cents/gallon
D) 222.7 cents/gallon
E) 192.3 cents/gallon
Version B KEY – Page 11 of 17
MATH 1010
Essential Mathematics
Test 2
Version B KEY
Spring 2016
Sections 3D – 5A
18. You would like to purchase a used car, but you need a loan to complete the
transaction. The car dealership has offered you a loan at an APR of 4.8%
compounded monthly for 3 years. If you can afford to make payments of $200 per
month, what is the price of the most expensive car you can afford to purchase?
Round your answer to the nearest whole dollar.
A) $7728
B) $6693
C) $8237
D) $7200
E) $7546
19. A market research firm interviews a random sample of 2500 adults.
Result: 66% find shopping for clothes frustrating and time consuming.
Identify the underlined numbers.
A) 2500 is the population size and 66% is the sample statistic.
B) 2500 is the sample size and 66% is the population parameter.
C) 2500 is the sample size and 66% is the sample statistic.
D) 2500 is the population size and 66% is the margin of error.
E) 2500 is the population size and 66% is the population parameter.
20. Tim is in the 35% tax bracket and claims the standard deduction. How much will his
tax bill be reduced if he qualifies for a $468 tax credit?
A) $468.00
B) $304.20
C) $163.80
D) $0
E) $117.00
Version B KEY – Page 12 of 17
Test 2
Version B KEY
MATH 1010
Essential Mathematics
Spring 2016
Sections 3D – 5A
Free Response Portion
Show all necessary work. Verify that the answers carry the appropriate units.
Partial credit may be given for work towards the correct solution.
However, if answers are shown without necessary work,
YOU MAY RECEIVE LITTLE OR NO CREDIT FOR THE CORRECT ANSWER.
1.
Matthew wants to invest $6,000 over a 5 year time period. He is considering two
options for this investment.
Option 1:
Option 2:
a.
Deposit $6,000 into a savings account with APR of 5.5% compounded
daily (365 times per year)
Deposit $100 per month into a savings plan with APR of 7%
compounded monthly
Complete the following table.
Options
Opt 1
Opt 2
Formula to Compute the
Amount in the Account
Work
(Substitute values into each
formula.)
(Do not substitute any values.)
APR 

A = P1 +
n 


 1 +

A = PMT  



(nY )
APR 

n 
(nY )
 APR 


 n 

− 1 






.055 

6000  1 +
365 


  1 +

100  



.07 

12 
( 365×5 )
(12×5 )
 .07 


 12 

− 1 






Amount in
Account after
5 Years
(Round answers
to the nearest
cent.)
$7,899.02
$7,159.29
1 point per formula (Graded all or nothing.)
1 point per substitutions into formula, if reasonable following work
1 point per amount in account, following work from substitutions
–½ if minor error in formula substitutions
–½ if amount rounded incorrectly
b.
Which option should Matthew choose to make the most of his investment?
Circle one: Option 1
OR
Option 2
1 point, following part a.
Points earned on this question:
Available points on this question:
7
Version B KEY – Page 13 of 17
MATH 1010
Essential Mathematics
2.
Test 2
Version B KEY
Spring 2016
Sections 3D – 5A
Suppose Adam had student loans totaling $24,000 when he graduated from
college. The interest rate is APR 5% compounded monthly and the loan term is 8
years. SHOW ALL WORK and round answers to the nearest cent, if necessary.
a.
Calculate Adam’s monthly payment.
 .05 
24000 

 12 
PMT =
= $303.84
( −12×8 ) 
 
.05 
1 −  1 +


12 
 

1 point for formula (Graded all or nothing.)
1 point for substitutions into formula, if reasonable following work
1 point for payment amount, following work from substitutions
–½ if minor error in formula substitutions
–½ if amount rounded incorrectly
b.
303.84
Monthly Payment (8-Year Payoff): $ _______________
How much will he pay over the lifetime of the loan?
Use your rounded answer from part (a).
Total Payments = $303.84 × 12 × 8 = $29,168.64
2 points (1 pt. for work, 1 pt. for total payments)
c.
29,168.64
Total of Payments (8-Year Payoff): $ _______________
Of the total amount paid, how much is paid in interest?
Interest = $29,168.64 – $24,000 = $5,168.64
2 points (1 pt. for work, 1 pt. for interest)
d.
5,168.64
Interest (8-Year Payoff): $ _______________
If Adam decides to pay off his loan in 6 years instead of 8 years, then his new
monthly payment will be $386.52. How much will he pay over the lifetime of the
loan if he pays it off in 6 years?
Total Payments = $386.52 × 12 × 6 = $27,829.44
2 points (1 pt. for work, 1 pt. for total payments)
e.
27,829.44
Total of Payments (6-Year Payoff): $ _______________
How much will Adam save by paying off the loan in 6 years instead of 8 years?
Interest = $29,168.64 – $27,829.44 = $1,339.20
2 points (1 pt. for work, 1 pt. for total payments)
1,339.20
Savings: $ _______________
Points earned on this question:
Available points on this question:
11
Version B KEY – Page 14 of 17
Test 2
Version B KEY
MATH 1010
Essential Mathematics
3.
Spring 2016
Sections 3D – 5A
Bob and Carol are married and filing jointly. Their (combined) taxable income last
year was $93,500. They received a tax credit of $2,000.
a.
Find Bob and Carol's Total Income Tax.
Show ALL work and round your answer to the nearest cent.
Rates 10%
Married, $17,850
Filing Jointly
Cutoffs
15%
$72,500
25%
28%
$146,400
$93,500 (Bob and Carol)
33%
$223,050
10%(17850) + 15%(72500-17850) + 25%(93500-72500) = $15,232.50
Apply tax credit: Total Income Tax = $15,232.50 – $2,000 = $13,232.50
4 points for tax calculated from table, details below:
[0 points for no reasonable work,
1 point for incorrect with a little reasonable work,
2 points for about half correct,
3 points for mostly correct,
4 points for completely correct]
–1 if tax calculation is started with wrong taxable income
–½ if minor error
–3 if no work shown, but answer correct
1 point for (implicitly or explicitly) subtracting the tax credit, following work
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
13,232.50
Total Income Tax: $ _______________
b.
Bob and Carol’s (combined) wages were $117,500 and they earned $5,320
from investments. Bob and Carol’s FICA tax was $8,988.75.
Find Bob and Carol's Tax Bracket and Overall Federal Tax Rate.
Show work for the Overall Fed Tax Rate and round your answer to one decimal place.
Fed. Tax Rate =
13232.50 + 8988.75
22220.75
× 100% =
× 100% = 18.1%
117500 + 5320
122820
3 points (2 pts formula and substitutions, following work, 1 pt answer)
–1 if numerator or denominator substitutions are incorrect
1 point, following part a.
25
Tax Bracket: _______________
%
18.1
Overall Federal Tax Rate: _______________
%
Points earned on this question:
Available points on this question:
9
Version B KEY – Page 15 of 17
MATH 1010
Essential Mathematics
4.
Test 2
Version B KEY
Spring 2016
Sections 3D – 5A
In a high school with over 600 students enrolled, 450 students responded to a
survey about sleep. Of those responding to the survey, 320 students said that they
sleep more than 20 hours each weekend.
a.
Identify parts of the sample.
1 point per Population and
High School’s enrolled students
Population: ________________________________________
Sample (reasonably close)
450 students surveyed
Sample: ________________________________________
71.1
Sample Statistic: __________%
(Show work below and round your answer to one decimal place.)
320
SS =
×100% = 71.1%
450
3 points (1 pt per substitution in numerator and denominator, 1 point answer)
–½ if answer not rounded correctly
b.
Find the margin of error. Show work and round the percentage to one decimal place.
1
Margin of Error =
×100% = 4.7%
450
3 points for MOE (1 pt formula, 1 pt. substitution, 1 point answer)
–½ if answer not rounded correctly
4.7
Margin of Error: _______________%
c.
Find the 95% confidence interval for the percentage of students who sleep
more than 20 hours each weekend. Show work and round values to one decimal
place.
CI = [ (71.1 – 4.7)%, (71.1 + 4.7)% ]
2 point for each endpoint in CI (1 pt work, 1 pt answer)
–1 if endpoints switched in interval
66.4
75.8
Confidence Interval: [ _________
%, _________%
]
Points earned on this question:
Available points on this question:
12
Version B KEY – Page 16 of 17
MATH 1010
Essential Mathematics
Test 2
Version B KEY
Spring 2016
Sections 3D – 5A
Scantron (1 pt.)
Check to make sure your Scantron form meets the following criteria. If any of the
items are NOT satisfied when your Scantron is handed in and/or when your
Scantron is processed one point will be subtracted from your test total.
My Scantron:
□ is bubbled with firm marks so that the form can be machine read;
□ is not damaged and has no stray marks (the form can be machine read);
□ has 20 bubbled in answers;
□ has MATH 1010 and my Section number written at the top;
□ has my Instructor’s name written at the top;
□ has Test No. 2 written at the top;
□ has Test Version B both written at the top and bubbled in below my CUID;
□ and shows my correct XID written in and then bubbled in with a zero in the first
column followed by the eight digits.
Version B KEY – Page 17 of 17