Question

Joe is getting ready to buy a car. At the same time, he has $23,000 in investments earning 5.0% annually. The car also costs $23,000. If he doesn't pay cash for the car, Joe can get a loan at 4.3% interest for 4 years. The loan is structured so that Joe pays one final payment at the end of 4 years. The final payment includes the principal plus all interest accrued over 4 years. If Joe takes the loan will he have enough money available from his investments to make the final payment? How much will he be short/have to spare? A. Yes; $650.79 B. No; $738.09 C. Yes; $738.09 D. No; $650.79

Answer 1

- Current Investment of Joe = $23,000

Calculating the Future Value of Joe's Investment after 4 years:-

Future Value = Invested Amount*(1+r)^n

Where,

r = Periodic Interest rate = 5%

n= no of periods = 4 years

Future Value = $23,000*(1+0.05)^4

Future Value = $23,000*1.21550625

Future Value = $27956.64

So, value at the end of year 4of joe's Investment is $27,956.64

- Now, Joe takes loan of $23,000 at interest rate of 4.3%

Calculating the Value of Loan payment at the end of year 4 including the principal plus all interest accrued over 4 years:-

Final Payment= Loan Amount*(1+r)^n

Where,

r = Periodic Interest rate = 4.3%

n= no of periods = 4 years

Final Payment= $23,000*(1+0.043)^4

Final Payment= $23,000*1.1834154468

Final Payment= $27218.56

So, Final Payment of Loan is $27218.56

So, Amount of money Joe will have at the end of year 4 after repayment of loan = $27,956.64 - $27,218.56

= $738.08

So, Joe will have Spare $738.08 left after loan repayment.

Option C

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