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Exam 28: Time Value of Money

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Question 31

Multiple Choice

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The store where you bought new home furnishings offers you two alternative payment plans. The first plan requires a $4,000 immediate up-front payment. The second plan requires you to make monthly payments of $137.41, payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly payment plan?

A) 12.31%
B) 12.96%
C) 13.64%
D) 14.36%
E) 15.08%

F) D) and E)
G) A) and D)

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Question 32

Multiple Choice

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How much would $100, growing at 5% per year, be worth after 75 years?

A) $3,689.11
B) $3,883.27
C) $4,077.43
D) $4,281.30
E) $4,495.37

F) B) and D)
G) B) and C)

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Question 33

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Suppose Sally Smith plans to invest $1,000. She can earn an effective annual rate of 5% on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

Billy Thornton borrowed $20,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Billy have to pay in a 30-day month?

As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or less than the nominal rate on the deposit (or loan).

You were left $100,000 in a trust fund set up by your grandfather. The fund pays 6.5% interest. You must spend the money on your college education, and you must withdraw the money in 4 equal installments, beginning immediately. How much could you withdraw today and at the beginning of each of the next 3 years and end up with zero in the account?

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year.

After receiving a reward for information leading to the arrest of a notorious criminal, you are considering investing it in an annuity that pays $5,000 at the end of each year for 20 years. You could earn 5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Which of the following statements is CORRECT?

Suppose you deposited $5,000 in a bank account that pays 5.25% with daily compounding based on a 360-day year. How much would be in the account after 8 months, assuming each month has 30 days?

As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or greater than the nominal rate on the deposit (or loan).

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the beginning of each of the next 20 years?

A time line is not meaningful unless all cash flows occur annually.

Starting to invest early for retirement increases the benefits of compound interest.

Suppose your credit card issuer states that it charges a 15.00% nominal annual rate, but you must make monthly payments, which amounts to monthly compounding. What is the effective annual rate?

Some of the cash flows shown on a time line can be in the form of annuity payments while others can be uneven amounts.

Which of the following statements is CORRECT, assuming positive interest rates and holding other things constant?

What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%?

Your sister paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years, then an additional lump sum payment of $10,000 at the end of the 5th year. What is the expected rate of return on this investment?

The going rate of interest on a 5-year treasury bond is 4.25%. You have one that will pay $2,500 five years from now. How much is the bond worth today?