Question 1

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 + (.07/4)]⁴ - 1 = .0719, or 7.19%EAR = [1 + (.068/12)]¹² - 1 = .0702, or 7.02%EAR = [1 + (.072/52)]⁵² - 1 = .0746, or 7.46%EAR = APR = 7.5%

Question 2

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

Question 3

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 on a loan must be equal to the effective annual rate when compounding occurs annually. This is because the APR takes into account the interest rate charged on the loan, as well as any fees or charges associated with the loan, expressed as an annual percentage rate. The effective annual rate, on the other hand, takes into account the effect of compounding over the course of a year, and reflects the true annual cost of the loan. When compounding occurs annually, the APR and the effective annual rate will be the same.

Question 4

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 + .0125)¹² - 1 = .1608, or 16.08%APR = 1.25% × 12 = 15.00%

Question 5

Discuss the statement, "Money has a time value."

Accepted Answer

The answer of Discuss the statement, "Money has a time...

Question 6

Some home loans involve "points," which are fees charged by the lender. Each point charged means that the borrower must pay 1% of the loan amount as a fee. For example, if 0.5 point is charged on a $100,000 loan, the loan repayment schedule is calculated on the $100,000 loan, but the net amount the borrower receives is only $99,500. What is the effective annual interest rate charged on such a loan, assuming that loan repayment occurs over 360 months, and that the interest rate is 1% per month? (Round the monthly payment amount to 2 decimal places.)

Accepted Answer

The answer of Some home loans involve "points," which are...

Question 7

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 8

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/(.0565/12)] - 1/{(.0565/12)[1 + (.0565/12)]^{30 × 12}})PMT = $865.85$150,000 = PMT([1/(.049/12)] - 1/{(.049/12)[1 + (.049/12)]^{15 × 12}})PMT = $1,178.39Total difference = ($865.85 × 12 × 30) - ($1,178.39 × 12 × 15) = $99,595.80

Question 9

What problem can be caused by "mixing" real and nominal cash flows in discounting exercises?

Accepted Answer

The answer of What problem can be caused by "mixing"...

Question 10

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 could only earn 8% rather than the 11% you had hoped to earn on your savings?
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 11

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 9% interest versus a 15-year mortgage with 8.5% interest. 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) $112,410
D)$124,300

Accepted Answer

$100,000 = PMT([1/(.09/12)] - 1/{(.09/12)[1 + (.09/12)]^{30 × 12}})PMT = $804.62$100,000 = PMT([1/(.085/12)] - 1/{(.085/12)[1 + (.085/12)]^{15 × 12}})PMT = $984.74Total difference = ($804.62 × 12 × 30) - ($984.74 × 12 × 15) = $112,410

Question 12

How should we compare interest rates quoted over different time intervals-for example, monthly versus annual rates?

Accepted Answer

The answer of How should we compare interest rates quoted...

Question 13

Why is it difficult and perhaps risky to evaluate financial projects based on APR alone?

Accepted Answer

The answer of Why is it difficult and perhaps risky...

Question 14

What is the difference between real and nominal cash flows and between real and nominal interest rates?

Accepted Answer

The answer of What is the difference between real and...

Question 15

Discuss the statement, "It is always preferred to select an account that offers compound interest over an account that offers simple interest."

Accepted Answer

The answer of Discuss the statement, "It is always preferred...

Question 16

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, r = .0075APR = .0075 × 12APR = .09, or 9%

Question 17

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 = .1956, or 19.56%

Question 18

Prizes are often not "worth" as much as claimed. Place a value on a prize of $5,000,000 that is to be received in equal payments over 20 years, 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/.07) - [1/.07(1.07)²⁰]}) × (1.07)PV = $2,833,898.81

Question 19

Show numerically that a savings account with a current balance of $1,000 that earns interest at 9% annually is precisely sufficient to make the payments on a 3-year loan of $1,000 that carries equal annual payments at 9% interest.

Accepted Answer

The answer of Show numerically that a savings account with...

Quiz 5: The Time Value of Money

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?

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%?

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

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 .

Discuss the statement, "Money has a time value."

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?

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.)

What problem can be caused by "mixing" real and nominal cash flows in discounting exercises?

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 could only earn 8% rather than the 11% you had hoped to earn on your savings?

How should we compare interest rates quoted over different time intervals-for example, monthly versus annual rates?

Why is it difficult and perhaps risky to evaluate financial projects based on APR alone?

What is the difference between real and nominal cash flows and between real and nominal interest rates?

Discuss the statement, "It is always preferred to select an account that offers compound interest over an account that offers simple interest."

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?

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

Show numerically that a savings account with a current balance of $1,000 that earns interest at 9% annually is precisely sufficient to make the payments on a 3-year loan of $1,000 that carries equal annual payments at 9% interest.