Answered Essay: Keith Bowie is trying to determine the amount to set aside so that he will have enough mo

Exercise 6-21

Keith Bowie is trying to determine the amount to set aside so that he will have enough money on hand in 4 years to overhaul the engine on his vintage used car. While there is some uncertainty about the cost of engine overhauls in 4 years, by conducting some research online, Keith has developed the following estimates.

Engine Overhaul
Estimated Cash Outflow
Probability
Assessment
$300 10 %
500 30 %
750 50 %
990 10 %

(Use the tables below.)


How much should Keith Bowie deposit today in an account earning 8%, compounded annually, so that he will have enough money on hand in 4 years to pay for the overhaul? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,581.)

Deposit amount $

Expert Answer

 

The estimate for the cost of overhaul of engine is :- 300 * 10 % + 500 * 30 % + 750 * 50 % + 990 * 10 % = 30 + 150 + 375 + 99 = $ 654

Now, given i = 8 % and time = 4 years

We need $ 654 after 4 years so we need to find out the present value of $ 654 in order to know the amount to be deposited today :-

654 * PVIF ( 8 % , 4 years )

654 * 0.735 = $ 480 ( answer )

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