Exam 4: Time Value of Money

Suppose the U.S. Treasury offers to sell you a bond for $3,000. No payments will be made until the bond matures 10 years from now, at which time it will be redeemed for $5,000. What interest rate would you earn if you bought this bond at the offer price?

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.

You borrowed $50,000 which you must repay in 10 years. You plan to make an initial deposit today, then make 9 more deposits at the beginning of each the next 9 years, but with the deposits increasing at the inflation rate. You expect to earn 5% on your funds, and you expect a 3% inflation rate. To the nearest dollar, how large must your initial deposit be to enable you to reach your $50,000 target?

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?

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?

Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly.

At a rate of 6.5%, what is the future value of the following cash flow stream?

Pacific Bank pays a 4.50% nominal rate on deposits, with monthly compounding. What effective annual rate (EFF%) does the bank pay?

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

Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.

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

Your sister turned 35 today, and she is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year.

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

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.

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

Which of the following investments would have the lowest present value? Assume that the effective annual rate for all investments is the same and is greater than zero.

All other things held constant, the present value of a given annual annuity decreases as the number of periods per year increases.

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.)

Last year Tempe Corporation's sales were $525 million. If sales grow at 7.5% per year, how large (in millions) will they be 8 years later?

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