Question Future Value of a Lump Sum

Future Value of a Lump Sum

P3-1. You have $1,500 to invest today at 7 percent interest compounded annually.

a. How much will you have accumulated in the account at the end of the following number of years?

1. Three years

2. Six years

3. Nine years

b. Use your findings in part (a) to calculate the amount of interest earned in

1. the first three years (years 1 to 3)

2. the second three years (years 4 to 6)

3. the third three years (years 7 to 9)

c. Compare and contrast your findings in part (b). Explain why the amount of interest earned increases in each succeeding 3-year period.

Present Value of a Lump Sum

P3-2. You just won a lottery that promises to pay you $1 million exactly 10 years from today. Because the $1 million payment is guaranteed by the state in which you live, opportunities exist to sell the claim today for an immediate lump-sum cash payment.

a. What is the least you will sell your claim for if you could earn the following rates of return on similar-risk investments during the 10-year period?

1. 6 percent

2. 9 percent

3. 12 percent

b. Rework part (a) under the assumption that the $1 million payment will be received in 15 rather than 10 years.

c. Based on your findings in parts (a) and (b), discuss the effect of both the size of the rate of return and the time until receipt of payment on the present value of a future sum.

P3-3. An Indiana state savings bond can be converted to $100 at maturity six years from purchase. If the state bonds are to be competitive with U.S. savings bonds, which pay 8 percent annual interest (compounded annually), at what price must the state sell its bonds? Ignore taxes and assume no cash payments on savings bonds prior to redemption.

Future Value of Cash Flow Streams

P3-4. Kim Edwards and Chris Phillips are both newly minted 30-year old MBAs. Kim plans to invest $1,000 per month into her 401(k) beginning next month, while Chris intends to invest $2,000 per month, but he does not plan to begin investing until 10 years after Kim begins investing. Both Kim and Chris will retire at age 67, and the 401(k) plan averages a 12 percent annual return compounded monthly. Who will have more 401(k) money at retirement?

P3-5. Robert Williams is considering an offer to sell his medical practice, allowing him to retire five years early. He has been offered $500,000 for his practice and can invest this amount in an account earning 10 percent per year, compounded annually. If the practice is expected to generate the following cash flows, should Robert accept this offer and retire now?

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