Question

Leon Bowie is trying to determine the amount to set aside so that he will have...

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%



Click here to view factor tables

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

Homework Answers

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
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