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Exam 28: Time Value of Money

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Question 51

Multiple Choice

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Ellen now has $125. How much would she have after 8 years if she leaves it invested at 8.5% with annual compounding?

A) $205.83
B) $216.67
C) $228.07
D) $240.08
E) $252.08

F) D) and E)
G) B) and D)

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Question 52

Multiple Choice

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Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2?

A) $7,531
B) $7,927
C) $8,323
D) $8,740
E) $9,177

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

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Question 53

Multiple Choice

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Suppose a State of North Carolina bond will pay $1,000 ten years from now. If the going interest rate on these 10-year bonds is 5.5%, how much is the bond worth today?

Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?

Southwestern Bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Woodburn Bank also offers to lend you the $50,000, but it will charge an annual rate of 7.0%, with no interest due until the end of the year. How much higher or lower is the effective annual rate charged by Woodburn versus the rate charged by Southwestern?

Some of the cash flows shown on a time line can be in the form of annuity payments but none can be uneven amounts.

Suppose Randy Jones plans to invest $1,000. He 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 somewhat less than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs annually.)

Your aunt has $500,000 invested at 5.5%, and she now wants to retire. She wants to withdraw $45,000 at the beginning of each year, beginning immediately. When she makes her last withdrawal (at the beginning of a year) , she also wants to have enough left in the account so that you can make a final withdrawal of $50,000 at the end of that year (her last withdrawal is at the beginning of the year, your withdrawal is at the end of that same year) . What is the maximum number of $45,000 withdrawals that she can make and still have enough in the account so that you can make a $50,000 withdrawal at the end of the year of her last withdrawal? (Hint: If your solution for N is not an integer, round down to the nearest whole number.)

You are considering two equally risky annuities, each of which pays $25,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?

What's the future value of $1,200 after 5 years if the appropriate interest rate is 6%, compounded monthly?

If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series.

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

Suppose United Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year. What is the effective annual rate on the loan?

How much would $20,000 due in 50 years be worth today if the discount rate were 7.5%?

Suppose you just won the state lottery, and you have a choice between receiving $2,550,000 today or a 20-year annuity of $250,000, with the first payment coming one year from today. What rate of return is built into the annuity? Disregard taxes.

You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12 quarters) from now?

Your bank pays 4% interest annually. You have $2,500 invested in the bank. How long will it take for your funds to double?

Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value.

Your bank account pays an 8% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

Which of the following statements regarding a 15-year (180-month) $225,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)