Question

Morgan Bowie is trying to determine the amount to set aside so that he will have enough money on hand in 3 years to overhaul the engine on his vintage used car. While there is some uncertainty about the cost of engine overhauls in 3 years, by conducting some research online, Morgan has developed the following estimates.
Engine Overhaul Estimated Cash Outflow Probability Assessment
$390 10%
570 30%
750 50%
790 10%


How much should Keith Bowie deposit today in an account earning 6%, compounded annually, so that he will have enough money on hand in 6 years to pay for the overhaul?

Answer 1

Answer:

$468.09

Step-by-step explanation:

first we must calculate the expected future value of the engine overhaul:

($390 x 10%) + ($570 x 30%) + ($750 x 50%) + ($790 x 10%) = $39 + $171 + $375 + $79 = $664

now we must determine the present value of $664 using a 6% interest rate:

PV = FV / (1 + r)⁶ = $664 / 1.06⁶ = $468.09