# chapter 6 the time value of money

Chapter 6 the time value of money

1. The Lexington Property Development Company has a \$ 10,000 note receivable from a customer due in three years. How much is the note worth today if the interest rate is

a. 9%?

b. 12% compounded monthly?

c. 8% compounded quarterly?

d. 18% compounded monthly?

e. 7% compounded continuously?

2. What will a deposit of \$ 4,500 left in the bank be worth under the following conditions?

a. Left for nine years at 7% interest

b. Left for six years at 10% compounded semiannually

c. Left for five years at 8% compounded quarterly

d. Left for 10 years at 12% compounded monthly

3. What interest rates are implied by the following lending arrangements?

a. You borrow \$ 500 and repay \$ 555 in one year.

b. You lend \$ 1,850 and are repaid \$ 2,078.66 in two years.

c. You lend \$ 750 and are repaid \$ 1,114.46 in five years with quarterly compounding.

d. You borrow \$ 12,500 and repay \$ 21,364.24 in three years under monthly compounding.

( Note: In parts c and d, be sure to give your answer as the annual nominal rate.)

4. How long does it take for the following to happen?

a. \$ 856 grows into \$ 1,122 at 7%

b. \$ 450 grows into \$ 725.50 at 12% compounded monthly

c. \$ 5,000 grows into \$ 6,724.44 at 10% compounded quarterly

5. Sally Guthrie is looking for an investment vehicle that will double her money in five years.

a. What interest rate, to the nearest whole percentage, does she have to receive?

b. At that rate, how long will it take the money to triple?

c. If she cant find anything that pays more than 11%, approximately how long will it take to double her investment?

d. What kind of financial instruments do you think Sally is looking at? Are they risky? What could happen to Sallys investment?

7. John Cleavers grandfather died recently and left him a trunk that had been locked in his attic for years. At the bottom of the trunk John found a packet of 50 World War I liberty bonds that had never been cashed in. The bonds were purchased for \$ 11.50 each in 1918 and pay 3% interest as long as theyre held. ( Government savings bonds like these accumulate and compound their interest, unlike corporate bonds which regularly pay out interest to bond holders.)

a. How much were the bonds worth in 2007?

b. How much would they have been worth if they paid interest at a rate more like that paid during the 1970s and 80s, say 7%?

c. Comment on the difference between the answers to parts ( a) and ( b).

9. Charlie owes Joe \$ 8,000 on a note that is due in five years with accumulated interest at 6%. Joe has an investment opportunity now that he thinks will earn 18%. Theres a chance, however, that it will earn as little as 4%. A bank has offered to discount the note at 14% and give Joe cash that he can invest today.

a. How much ahead will Joe be if he takes the banks offer and the investment does turn out to yield 18%?

b. How much behind will he be if the investment turns out to yield only 4%?

10. Ralph Renner just borrowed \$ 30,000 to pay for a new sports car. He took out a 60- month loan and his car payments are \$ 761.80 per month. What is the effec-tive annual interest rate ( EAR) on Ralphs loan?

Annuity Problems

11. How much will \$ 650 per year be worth in eight years at interest rates of

a. 12%?

b. 8%?

c. 6%?

12. The Wintergreens are planning ahead for their sons education. Hes eight now and will start college in 10 years. How much will they have to set aside each year to have \$ 65,000 when he starts if the interest rate is 7%?

13. What interest rate would you need to get to have an annuity of \$ 7,500 per year accumulate to \$ 279,600 in 15 years?

14. How many years will it take for \$ 850 per year to amount to \$ 20,000 if the interest rate is 8%?

15. What would you pay for an annuity of \$ 2,000 paid every six months for 12 years

17. A \$ 10,000 car loan has payments of \$ 361.52 per month for three years. What is the interest rate? Assume monthly compounding and give the answer in terms of an annual rate.

18. Joe Ferros uncle is going to give him \$ 250 a month for the next two years starting today. If Joe banks every payment in an account paying 6% compounded monthly, how much will he have at the end of three years?

19. How long will it take a payment of \$ 500 per quarter to amortize a loan of \$ 8,000 at 16% compounded quarterly? Approximate your answer in terms of years and months. How much less time will it take if loan payments are made at the begin-ning of each quarter rather than at the end?

20. Ryan and Laurie Middleton just purchased their first home with a traditional ( monthly compounding and payments) 6% 30- year mortgage loan of \$ 178,000.

a. How much is their monthly payment?

b. How much interest will they pay the first month?

26. Amys uncle died recently and left her some money in a trust that will pay her \$ 500 per month for five years starting on her 25th birthday. Amy is getting mar-ried soon, and she would like to use this money as a down payment on a house now. If the trust allows her to assign its future payments to a bank, and her bank is willing to discount them at 9% compounded monthly, how much will she have toward her down payment on home ownership? Amy just turned 23.

27. Lee Childs is negotiating a contract to do some work for Haas Corp. over the next five years. Haas proposes to pay Lee \$ 10,000 at the end of each of the third, fourth, and fifth years. No payments will be received prior to that time. If Lee dis-counts these payments at 8%, what is the contract worth to him today?

29. The Orion Corp. is evaluating a proposal for a new project. It will cost \$ 50,000 to get the undertaking started. The project will then generate cash inflows of \$ 20,000 in its first year and \$ 16,000 per year in the next five years, after whichit will end. Orion uses an interest rate of 15% compounded annually for such evaluations.

a. Calculate the net present value ( NPV) of the project by treating the initial cost as a cash outflow ( a negative) in the present, and adding the present value of the subsequent cash inflows as positives.

b. What is the implication of a positive NPV? ( Words only.)

c. Suppose the inflows were somewhat lower, and the NPV turned out to be nega-tive. What would be the implication of that result? ( Words only.)

33. Joe Trenton expects to retire in 15 years and has suddenly realized that he hasnt saved anything toward that goal. After giving the matter some thought, he has decided that he would like to retire with enough money in savings to withdraw \$ 85,000 per year for 25 years after he retires. Assume a 6% return on investment before and after retirement and that all payments into and withdrawals from sav-ings are at year end.

a. How much does Joe have to save in each year for the next 15 years to reach this goal?

b. How much would Joe have needed to save each year if he had started when retirement was 25 years away?

c. Comment on the difference between the results of parts a and b.

37. Joan Colby is approaching retirement and plans to purchase a condominium in Florida in three years. She now has \$ 40,000 saved toward the purchase in a bank account that pays 8% compounded quarterly. She also has five \$ 1,000 face value corporate bonds that mature in two years. She plans to deposit the bonds princi-pal repayments in the same account when theyre paid. Joan also receives \$ 1,200 per month alimony from her ex- husband which will continue for two more years until he retires ( 24 checks including one that arrived today). Shes decided to put her remaining alimony money toward her condo, depositing it as received in a credit union account that pays 8% compounded monthly. Shell make the first deposit today with the check she already has. Joan anticipates buying a \$ 200,000 property. What will her monthly payment be on a 15- year mortgage at 6%? What would the payment be on a 30- year loan at the same interest rate?

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