Question

1. Suppose you invest $3,600 in an account bearing interest at the rate of 14 percent per year. What will be the future value of your investment in five years? 2. Your best friend won the state lottery and has offered to give you $11,100 in five years, after he has made his first million dollars. You figure that if you had the money today, you could invest it at 12 percent annual interest. What is the present value of your friend's future gift? 3. In four years, you would like to buy a small cabin in the mountains. You estimate that the property will cost you $63,500 when you are ready to buy. How much money would you need to invest each year in an account bearing interest at the rate of 6 percent per year in order to accumulate the $63,500 purchase price? 4. You have estimated that your educational expenses over the next four years will be $14,100 per year. How much money do you need in your account now in order to withdraw the required amount each year? Your account bears interest at 10 percent per year.

Answer 1

Part 1

Future value = PV*(1+r)^n = 3600*(1.14^5) = $6931.49

Part 2

Present value = FV/(1+r)^n = 11100/(1.12^5) = $6298.44

Part 3

Annual investment = FV/FVIFA

FVIFA = ((1+r)^n -1)/r

Annual investment = 63500/(((1.06^4)-1)/6%) = $14515.56

Part 4

PV = annual expenses * PVIFA

PVIFA = ((1-(1+r)^-n)/r)

PV = 14100*((1-(1.10^-4))/10%) = $44695.10