Question

5. (8 points) Calculate the following time value of money problems. a. What is the future value of 22 periodic payments of $7,520 each made at the beginning of each period and compounded at 8% per period? b. What would you pay for a $500,000 face value bond that matures in 15 years and pays $40,000 a year in interest (end-of-period payments) if you wanted to earn a yield of 9%. C. Mike Finley wishes to become a millionaire. His money market fund has a balance of $555,264.50 and has a guaranteed interest rate of 4%. How many years must Mike leave that balance in the fund in order to get his desired $1,000,000? d. Andrew Bogut just received a signing bonus of $1,000,000. His plan is to invest this payment in a fund for 8 years (his planned retirement date). If Bogut plans to establish the AB Foundation once the fund grows to $1,850,930, what annually compounded interest rate must he earn to achieve his goal?

Answer 1

a. Answer : $ 450,397.62

Future value interest factor of an annuity due = [ {( 1 + r ) ⁿ - 1} / r ] * ( 1 + r )

If r = 0.08 and n = 22, FVIFA of annuity due = [ { ( 1.08 ) ²² - 1 } / 0.08 ] * 1.08 = 59.8933

If the annuity at the beginning of each period is $ 7,520, Future Value = $ 7,520 x 59.8933 = $ 450,397.62

b. Answer: $ 459,678

Maturity amount : $ 500,000

Annual coupon : $ 40,000.

i : 9 %

n = 15

PV _{9%, n=15} = ( 1 / 1.09 ) ¹⁵ = 0.2745

PVA _{9%, n=15}  = [ 1 - ( 1 / 1.09 ) ¹⁵ } / 0.09 ] = 8.0607

Present value of the bonds = $ 40,000 x 8.0607 + $ 500,000 x 0.2745 =$ 322,428 + $ 137,250 = $ 459,678

c. Answer: 15 years.

FVIF = $ 1,000,000 / $ 555,264.50 = 1.80094

FVIF = ( 1.04 ) ⁿ = 1.80094

n = 15

d. Answer: 8 %

FVIF = $ 1,850,930 / $ 1,000,000 = 1.85093

FVIF = ( 1 + r ) ⁸ = 1.85093

( 1 + r ) = 1.07999

r = 0.07999 or 8 %