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Exam 5: Time Value of Money

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Question 81

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The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the smaller the present value of a given lump sum to be received at some future date.

A) True
B) False

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Question 82

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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.

A) True
B) False

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Question 83

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

You have a chance to buy an annuity that pays $2,500 at the end of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

Time lines cannot be constructed for annuities unless all the payments occur at the end of the periods.

You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded monthly. If you invest $3,000 at the end of each month, how many months will it take for your account to grow to $150,000?

Your father is about to retire, and he wants to buy an annuity that will provide him with $85,000 of income a year for 25 years, with the first payment coming immediately. The going rate on such annuities is 5.15%. How much would it cost him to buy the annuity 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?

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 investments would have the highest future value at the end of 10 years? Assume that the effective annual rate for all investments is the same and is greater than zero.

Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

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.

Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate.

You want to go to Europe 5 years from now, and you can save $3,100 per year, beginning one year from today. You plan to deposit the funds in a mutual fund that you think will return 8.5% per year. Under these conditions, how much would you have just after you make the 5th deposit, 5 years from now?

Your subscription to Investing Wisely Weekly is about to expire. You plan to subscribe to the magazine for the rest of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a lifetime subscription for $850, also payable immediately. Assuming that you can earn 6.0% on your funds and that the annual renewal rate will remain constant, how many years must you live to make the lifetime subscription the better buy?

You plan to borrow $35,000 at a 7.5% annual interest rate. The terms require you to amortize the loan with 7 equal end-of-year payments. How much interest would you be paying in Year 2?

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each of the next 5 years. By how much would you reduce the amount you owe in the first year?

Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 18.00%, with interest paid monthly, what is the card's EFF%?