Question 1

Miller's Hardware plans on saving $42,000,$54,000,and $58,000 at the end of each year for the next three years,respectively.How much will the firm have saved at the end of the three years if it can earn 4.5% on its savings?
A) $160,295.05
B) $158,098.15
C) $167,508.33
D) $165,212.57

Accepted Answer

FV = ($42,000 × 1.045²) + ($54,000 × 1.045) + $58,000FV = $160,295.05

Question 2

Prizes are often not "worth" as much as claimed.What is the value of a prize of $5,000,000 that is to be received in 20 equal yearly payments,with the first payment beginning today? Assume an interest rate of 7%.
A) $2,833,898.81
B) $2,911,015.68
C) $2,609,144.14
D) $2,738,304.13

Accepted Answer

Annual payment = $5,000,000 / 20 = $250,000PV = ($250,000 {(1 / 0.07) − [1 / 0.07(1.07)²⁰]}) × (1.07)PV = $2,833,898.81

Question 3

A credit card account that charges interest at the rate of 1.25% per month would have an annually compounded rate of _____ and an APR of ____.
A) 16.08%; 15.00%
B) 14.55%; 16.08%
C) 12.68%; 15.00%
D) 15.00%; 14.55%

Accepted Answer

EAR = (1 + 0.0125)¹² − 1 = 0.1608, or 16.08%APR = 1.25% × 12 = 15.00%

Question 4

The APR on a loan must be equal to the effective annual rate when:
A) compounding occurs monthly.
B) compounding occurs annually.
C) the loan is for less than one year.
D) the loan is for more than one year.

Accepted Answer

The APR and the effective annual rate will be equal when compounding occurs annually. If compounding occurs monthly, the effective annual rate will be higher than the APR due to the effect of compounding more frequently. If the loan is for less than one year, the effective annual rate cannot be calculated as it assumes compounding over a full year. If the loan is for more than one year, the effective annual rate may be different than the APR if the interest rate or compounding frequency changes over time.

Question 5

A car dealer offers payments of $522.59 per month for 48 months on a $25,000 car after making a $4,000 down payment.What is the loan's APR?
A) 6%
B) 9%
C) 11%
D) 12%

Accepted Answer

$25,000 − 4,000 = $522.59 {(1 / r) − [1 / r(1 + r)⁴⁸]}Using a financial calculator or Excel, r = 0.0075APR = 0.0075 × 12APR = 0.09, or 9%

Question 6

After reading the fine print in your credit card agreement,you find that the "low" interest rate is actually an 18% APR,or 1.5% per month.What is the effective annual rate?
A) 18.47%
B) 19.56%
C) 18.82%
D) 19.41%

Accepted Answer

EAR = 1.015¹² − 1 = 0.1956, or 19.56%

Question 7

Would you prefer a savings account that paid 7% interest compounded quarterly,6.8% compounded monthly,7.2% compounded weekly,or an account that paid 7.5% with annual compounding?
A) 7% compounded quarterly
B) 6.8% compounded monthly
C) 7.2% compounded weekly
D) 7.5% compounded annually

Accepted Answer

EAR = [1 + (0.07 / 4)]⁴ − 1 = 0.0719, or 7.19%EAR = [1 + (0.068 / 12)]¹² − 1 = 0.0702, or 7.02%EAR = [1 + (0.072 / 52)]⁵² − 1 = 0.0746, or 7.46%EAR = APR = 7.5%

Question 8

Eighteen years from now,4 years of college are expected to cost $150,000.How much more must be deposited into an account today to fund this expense if you can earn only 8% on your savings rather than the 11% you hope to earn?
A) $12,211.18
B) $13,609.21
C) $14,006.41
D) $14,614.03

Accepted Answer

Additional deposit = $150,000 / 1.08¹⁸ − $150,000 / 1.11¹⁸Additional deposit = $14,614.03

Question 9

A loan officer states,"Thousands of dollars can be saved by switching to a 15-year mortgage from a 30-year mortgage." Calculate the difference in payments on a 30-year mortgage at an interest rate of .75% a month versus a 15-year mortgage with an interest rate of .7% a month.Both mortgages are for $100,000 and have monthly payments.What is the difference in total dollars that will be paid to the lender under each loan? (Round the monthly payment amounts to 2 decimal places.)
A) $89,211
B) $98,406
C) $113,465
D) $124,300

Accepted Answer

$100,000 = PMT([1 / (0.0075)] − 1 / {(0.0075)[(1.0075)]^{30 × 12}})PMT = $804.62$100,000 = PMT([1 / (0.007)] − 1 / {(0.007 )[ 1.007)]^{15 × 12}})PMT = $ 978.87Total difference = ($804.62 × 12 × 30) − ($978.87 × 12 × 15) = $113,465

Question 10

You are considering the purchase of a home that would require a mortgage of $150,000.How much more in total interest will you pay if you select a 30-year mortgage at 5.65% rather than a 15-year mortgage at 4.9%? (Round the monthly payment amount to 2 decimal places.)
A) $86,311.18
B) $78,487.92
C) $99,595.80
D) $102,486.68

Accepted Answer

$150,000 = PMT([1 / (0.0565 / 12)] − 1 / {(0.0565 / 12)[1 + (0.0565 / 12)]^{30 × 12}})PMT = $865.85$150,000 = PMT([1 / (0.049 / 12)] − 1 / {(0.049 / 12)[1 + (0.049 / 12)]^{15 × 12}})PMT = $1,178.39Total difference = ($865.85 ×12 × 30) − ($1,178.39 × 12 × 15) = $99,595.80

Question 11

Lester's just signed a contract that will provide the firm with annual cash inflows of $28,000,$35,000,and $42,000 over the next three years with the first payment of $28,000 occurring one year from today.What is this contract worth today at a discount rate of 7.25%?
A) $88,311.08
B) $89,423.91
C) $90,580.55
D) $91,341.41

Accepted Answer

PV = $28,000 / 1.0725 + $35,000 / 1.0725² + $42,000 / 1.0725³PV = $90,580.55

Quiz 5: The Time Value of Money

Miller's Hardware plans on saving $42,000,$54,000,and $58,000 at the end of each year for the next three years,respectively.How much will the firm have saved at the end of the three years if it can earn 4.5% on its savings?

Prizes are often not "worth" as much as claimed.What is the value of a prize of $5,000,000 that is to be received in 20 equal yearly payments,with the first payment beginning today? Assume an interest rate of 7%.

A credit card account that charges interest at the rate of 1.25% per month would have an annually compounded rate of _ and an APR of .

The APR on a loan must be equal to the effective annual rate when:

A car dealer offers payments of $522.59 per month for 48 months on a $25,000 car after making a $4,000 down payment.What is the loan's APR?

After reading the fine print in your credit card agreement,you find that the "low" interest rate is actually an 18% APR,or 1.5% per month.What is the effective annual rate?

Would you prefer a savings account that paid 7% interest compounded quarterly,6.8% compounded monthly,7.2% compounded weekly,or an account that paid 7.5% with annual compounding?

Eighteen years from now,4 years of college are expected to cost $150,000.How much more must be deposited into an account today to fund this expense if you can earn only 8% on your savings rather than the 11% you hope to earn?

You are considering the purchase of a home that would require a mortgage of $150,000.How much more in total interest will you pay if you select a 30-year mortgage at 5.65% rather than a 15-year mortgage at 4.9%? (Round the monthly payment amount to 2 decimal places.)

Lester's just signed a contract that will provide the firm with annual cash inflows of $28,000,$35,000,and $42,000 over the next three years with the first payment of $28,000 occurring one year from today.What is this contract worth today at a discount rate of 7.25%?