Question

BE6-3 (L02) Candice Willis will invest $30,000 today. She needs $150,000 in 21 years. What annual interest rate must she earn?

BE6-6 (L03) Steve Madison needs $250,000 in 10 years. How much must he invest at the end of each year, at 5% interest, to meet his needs?

BE6-7 (L02) 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 8% (compounded annually) to buy the boat at retirement?

BE6-8 (L02) Refer to the data in BE6-7. Assuming quarterly compounding of amounts invested at 8%, how much of John Fillmore’s inheritance must be invested to have enough at retirement to buy the boat?

BE6-9 (L03) Morgan Freeman is investing $9,069 at the end of each year in a fund that earns 5% interest. In how many years will the fund be at $100,000?

BE6-15 (L05) 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?

Answer 1

Answer to BE6-3:

Amount invested = $30,000
Future value = $150,000
Period = 21 years

Let annual interest rate be i%

Amount invested * (1 + Interest rate)^Period = Future value
$30,000 * (1 + i)^21 = $150,000
(1 + i)^21 = 5
1 + i = 1.0797
i = 0.0797 or 7.97%

Interest rate = 7.97%

Answer to BE6-6:

Future value = $250,000
Period = 10 years
Interest rate = 5%

Let annual deposit be $x

$250,000 = $x*1.05^9 + $x*1.05^8 + … + $x*1.05 + $x
$250,000 = $x * (1.05^10 - 1) / 0.05
$250,000 = $x * 12.57789
$x = $19,876.14

Annual deposit = $19,876.14