John Davis, a recent IE graduate from Tennessee Technological University, bought

Question

John Davis, a recent IE graduate from Tennessee Technological University, bought an SUV for $30,000 with a down payment of $10,000. John had a little business on the side and did not have a girlfriend when he was at school and hence he was able to save the $10,000 for his dream car. He expects to take good care of the car and the dealership, owned by John’s uncle, agrees to take the car back for $8,000 at the end of 4 years. If the monthly payment is $400, what is the nominal interest rate on this loan? What is the effective interest rate?

Explanation / Answer

Down paymnet = $10000

Balance = $20000

Per month installment = $400

for a year, Installment = $400*12 = $4800

For 4 years, he pays $4800*4 = $19200

Salvage value at the end of 4 years = $8000

so, 30000-8000 = $22000

John paid $10000+19200 = $29200

For $22000 value after 4 years, he paid $29200

So 29200-22000=$7200

So $7200 Was the nominal interest paid by him for 4 years

$7200/48 = $150 per month

Therefore, $150/$400 = 37.5%

Effective interest rate = (1+.375)^12-1

=44.67%

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