Question

John 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, John has developed the following estimates.

Engine Overhaul Estimated Cash Outflow			Probability Assessment
$270			10%
630			30%
750			50%
870			10%

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How much should John 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?

Answer 1

Engine Overhaul Estimated Cash Outflow (x)		Probability Assessment (p)	xp
270		10%	27
630		30%	189
750		50%	375
870		10%	87
		total	678

In order to receive 678 $ @ end of 4 years @ 8% compounded annually,

V = a(1+r)ⁿ where V=value @ end of n years, a = amount invested, r = rate of int, n =no. of years

678 = a(1+0.08)⁴

So, A = 498.35.

So, John Bowie should deposit $498.35 today