Question & Answer

Presented below are three unrelated situations.

(a) Dwayne Wade Company recently signed a lease for a new office building, for a lease period of

10 years. Under the lease agreement, a security deposit of $12,000 is made, with the deposit to be returned at the expiration of the lease, with interest compounded at 10% per year. What amount will the company receive at the time the lease expires?

(b) Serena Williams Corporation, having recently issued a $20 million, 15-year bond issue, is committed to make annual sinking fund deposits of $600,000. The deposits are made on the last day of each year and yield a return of 10%. Will the fund at the end of 15 years be sufficient to retire the bonds?

If not, what will the deficiency be?

(c) Under the terms of his salary agreement, president Rex Walters has an option of receiving either an immediate bonus of $40,000, or a deferred bonus of $70,000 payable in 10 years. Ignoring tax considerations and assuming a relevant interest rate of 8%, which form of settlement should Walters accept?

Using the appropriate interest table, compute the present values of the following periodic amounts due at the end of the designated periods.

(a) $30,000 receivable at the end of each period for 8 periods compounded at 12%.

(b) $30,000 payments to be made at the end of each period for 16 periods at 9%.

(c) $30,000 payable at the end of the seventh, eighth, ninth, and tenth periods at 12%.

Using the appropriate interest table, answer the following questions. (Each case is independent of the others).

(a) What is the future value of 20 periodic payments of $4,000 each made at the beginning of eachperiod and compounded at 8%?

(b) What is the present value of $2,500 to be received at the beginning of each of 30 periods, discounted at 10% compound interest?

(c) What is the future value of 15 deposits of $2,000 each made at the beginning of each period and compounded at 10%? (Future value as of the end of the fifteenth period.)

(d) What is the present value of six receipts of $1,000 each received at the beginning of each period, discounted at 9% compounded interest?

Using the appropriate interest table, answer each of the following questions. (Each case is independent of the others.)

(a) What is the future value of $7,000 at the end of 5 periods at 8% compounded interest?

(b) What is the present value of $7,000 due 8 periods hence, discounted at 11%?

(c) What is the future value of 15 periodic payments of $7,000 each made at the end of each period and compounded at 10%?

(d) What is the present value of $7,000 to be received at the end of each of 20 periods, discounted at

5% compound interest?

Alan Jackson invests $20,000 at 8% annual interest, leaving the money invested without withdrawing any of the interest for 8 years. At the end of the 8 years,

Alan withdraws the accumulated amount of money.

Instructions

(a) Compute the amount Alan would withdraw assuming the investment earns simple interest.

(b) Compute the amount Alan would withdraw assuming the investment earns interest compounded annually.

(c) Compute the amount Alan would withdraw assuming the investment earns interest compounded semiannually.

For each of the following cases, indicate (a) to what rate columns, and (b) to what number of periods you would refer in looking up the interest factor.

1. In a future value of 1 table

Annual Number of

Rate Years Invested Compounded

a. 9% 9 Annually

b. 12% 5 Quarterly

c. 10% 15 Semiannually

2. In a present value of an annuity of 1 table

Annual Number of Number of Frequency of

Rate Years Involved Rents Involved Rents

a. 9% 25 25 Annually

b. 10% 15 30 Semiannually

c. 12% 7 28 Quarterly

Consider the loan in BE6-16. What payments must Zach Taylor make to settle the loan at the same interest rate but with the 6 payments beginning on the day the loan is signed?

Zach Taylor is settling a $20,000 loan due today by making 6 equal annual payments of $4,727.53.

Determine the interest rate on this loan, if the payments begin one year after the loan is signed.

Clancey Inc. issues $2,000,000 of 7% bonds due in 10 years with interest payable at year-end. The current market rate of interest for bonds of similar risk is 8%. What amount will Clancey receive when it issues the bonds?

Amy Monroe wants to create a fund today that will enable her to withdraw $25,000 per year for

8 years, with the first withdrawal to take place 5 years from today. If the fund earns 8% interest, how much must Amy invest today?

Adams Inc. will deposit $30,000 in a 12% fund at the end of each year for 8 years beginning December 31, 2014. What amount will be in the fund immediately after the last deposit?

Maria Alvarez is investing $300,000 in a fund that earns 8% interest compounded annually. What equal amounts can Maria withdraw at the end of each of the next 20 years?

Leon Tyler’s VISA balance is $793.15. He may pay it off in 12 equal end-of-month payments of $75 each. What interest rate is Leon paying?

Henry Quincy wants to withdraw $30,000 each year for 10 years from a fund that earns 8% interest.

How much must he invest today if the first withdrawal is at year-end? How much must he invest today if the first withdrawal takes place immediately?

Morgan Freeman is investing $16,380 at the end of each year in a fund that earns 10% interest. In how many years will the fund be at $100,000?

Refer to the data in BE6-7. Assuming quarterly compounding of amounts invested at 12%, how much of John Fillmore’s inheritance must be invested to have enough at retirement to buy the boat?

John Fillmore’s lifelong dream is to own his own fishing boat to use in his retirement. John has recently come into an inheritance of $400,000. He estimates that the boat he wants will cost $300,000 when he retires in 5 years. How much of his inheritance must he invest at an annual rate of 12% (compounded annually) to buy the boat at retirement?

Steve Madison needs $250,000 in 10 years. How much must he invest at the end of each year, at

11% interest, to meet his needs?

Sally Medavoy will invest $8,000 a year for 20 years in a fund that will earn 12% annual interest. If the first payment into the fund occurs today, what amount will be in the fund in 20 years? If the first payment occurs at year-end, what amount will be in the fund in 20 years?

Bo Newman will invest $10,000 today in a fund that earns 5% annual interest. How many years will it take for the fund to grow to $17,100?

Candice Willis will invest $30,000 today. She needs $150,000 in 21 years. What annual interest rate must she earn?

Tony Bautista needs $25,000 in 4 years. What amount must he invest today if his investment earns

12% compounded annually? What amount must he invest if his investment earns 12% annual interest compounded quarterly?

Chris Spear invested $15,000 today in a fund that earns 8% compounded annually. To what amount will the investment grow in 3 years? To what amount would the investment grow in 3 years if the fund earns 8% annual interest compounded semiannually?

Recently, property/casualty insurance companies have been criticized because they reserve for the total loss as much as 5 years before it may happen. The IRS has joined the debate because it says the full reserve is unfair from a taxation viewpoint. What do you believe is the IRS position?

Recently, Glenda Estes was interested in purchasing a Honda Acura. The salesperson indicated that the price of the car was either $27,600 cash or $6,900 at the end of each of 5 years. Compute the effective-interest rate to the nearest percent that Glenda would pay if she chooses to make the five annual payments.