chapter 6 finance 315

Which one of the following compounding periods will yield the lowest effective annual rate given a stated future value at Year 5 and an annual percentage rate of 10 percent?

annual

The interest rate that is most commonly quoted by a lender is referred to as the:

annual percentage rate.

Sara wants to establish a trust fund to provide $75,000 in scholarships each year and earn a fixed 6.15 percent rate of return. How much money must she contribute to the fund assuming that only the interest income is distributed?

$1,219,512 PV = $75,000/.0615 PV = $1,219,512

For the next 20 years, you plan to invest $600 a month in a stock account earning 7 percent and $400 a month in a bond account earning 4 percent. When you retire in 20 years, you will combine your money into an account with a return of 5 percent. How much can you withdraw each month during retirement assuming a 30-year withdrawal period?

$2,465.44 FVA = $600{[(1 + .07/12)(20)( 12) − 1]/(.07/12)} + $400{[(1 + .04/12) (20)(12) − 1]/(.04/12)} FVA = $459,265.85 PVA = $459,265.85 = C({1 − [1/(1 + .05/12)(30)(12)]}/(.05/12)) C = $2,465.44

Jones Stoneware has a liability of $75,000 due four years from today. The company is planning to make an initial deposit today into a savings account and then deposit an additional $10,000 at the end of each of the next four years. The account pays interest of 4.5 percent. How much does the firm need to deposit today for its savings to be sufficient to pay this debt?

$27,016.84 FVA = $10,000[(1.0454 − 1)/.045] FVA = $42,781.91 Additional FV needed = $75,000 − 42,781.91 Additional FV needed = $32,218.09 Initial deposit = $32,218.09/1.0454 Initial deposit = $27,016.84

Your grandfather left you an inheritance that will provide an annual income for the next 20 years. You will receive the first payment one year from now in the amount of $2,500. Every year after that, the payment amount will increase by 5 percent. What is your inheritance worth to you today if you can earn 7.5 percent on your investments?

$37,537.88 GAPV = $2,500{[1 −(1.05/1.075)20]/(.075 − .05)} GAPV = $37,537.88

You just won the magazine sweepstakes and opted to take unending payments. The first payment will be $50,000 and will be paid one year from today. Every year thereafter, the payments will increase by 2.5 percent annually. What is the present value of your prize at a discount rate of 7.9 percent?

$925,925.93 GPPV = $50,000/(.079 − .025) GPPV = $925,925.93

You are comparing two annuities that offer regular payments of $2,500 for five years and pay .75 percent interest per month. You will purchase one of these today with a single lump sum payment. Annuity A will pay you monthly, starting today, while annuity B will pay monthly, starting one month from today. Which one of the following statements is correct concerning these two annuities?

Annuity B has a smaller present value than annuity A.

Project A has cash flows of $4,000, $3,000, $0, and $3,000 for Years 1 to 4, respectively. Project B has cash flows of $2,000, $3,000, $2,000, and $3,000 for Years 1 to 4, respectively. Which one of the following statements is correct assuming the discount rate is positive? (No calculations needed)

Project B is worth less today than Project A.

A perpetuity is defined as:

unending equal payments paid at equal time intervals