Question

Leon Bowie is trying to determine the amount to set aside so that he will have enough money on hand in 6 years to overhaul the engine on his vintage used car. While there is some uncertainty about the cost of engine overhauls in 6 years, by conducting some research online, Leon has developed the following estimates.

Engine Overhaul Estimated Cash Outflow			Probability Assessment
$310			10%
510			30%
770			50%
760			10%

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How much should Leon Bowie deposit today in an account earning 9%, compounded annually, so that he will have enough money on hand in 6 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.)

For each of the following cases, indicate (a) to what rate columns, and (b) to what number of periods you would refer in looking up the interest factor.

1. In a future value of 1 table:

		Annual Rate		Number of Years Invested		Compounded		(a) Rate of Interest			(b) Number of Periods
a.		11%		9		Annually		enter percentages	%		enter the number of periods
b.		12%		6		Quarterly		enter percentages	%		enter the number of periods
c.		12%		19		Semiannually		enter percentages	%		enter the number of periods

2. In a present value of an annuity of 1 table: (Round answers to 1 decimal place, e.g. 458,58.1.)

		Annual Rate		Number of Years Invested		Number of Rents Involved		Frequency of Rents		(a) Rate of Interest			(b) Number of Periods
a.		9%		28		28		Annually		enter percentages	%		enter the number of periods
b.		10%		14		28		Semiannually		enter percentages	%		enter the number of periods
c.		12%		6		24		Quarterly		enter percentages	%		enter the number of periods

Answer 1

Calculation for Leon Bowie Deposit Today :

Estimated Cost of Engine Overhaul = Estimated Cash Outflow*Probability = $310*10% + 510*30% + 770*50% + 760*10%= $645

Present Value = [Future Value/(1+R)^n]

Therefore,Deposit Today to earn @ 9% in 6 years= [$645/(1+0.09)^6] = $645/1.67710 = $385

1)In a Future Value of 1 Table :

	Annual Rate	Number of Years Invested	Compunded	Rate of Interest	Number of Periods
a	11%	9	Annually	11%	9
b	12%	6	Quarterly	3%	24
c	12%	19	Semiannually	6%	38

2) In a Present Value of an annuity of 1 Table :

	Annual Rate	Number of Years Invested	Number of rents involved	Frequency	Rate of Interest	Number of Periods
a	9%	28	28	Annually	9%	28
b	10%	14	28	Semiannually	5%	28
c	11%	6	24	Quarterly	2.8%	24