Question

Kevin is trying to determine whether to lease or purchase a car. The purchase price is $42,000 and he has been approved for a 4- year loan with a 5.75% interest rate. He assumes the car's value will depreciate 8% each year, and he intends to sell the car after 10 years at the depreciated value.

What is his net gain or loss after selling the car?

$28,870.77
$65,359.41
$18,244.32
$47,115.09

Answer 1

Not a very good question.

Several missing pieces:
Do we have monthly payments?
Is the interest rate compounded monthly?
I will assume the case for both above.

We need the amount of the car payment:
42000 = paym( 1 - 1.00479166..^-48)/.004791666..
paym = $981.56

value of car after 10 years = 42000(.92)^10 = $18244.32
value of his 4 year's payments at the end of 10 years
= 981.56(1.00479166..^48 - 1)/.004791666... * 1.00479166..^72 = 52831.94
loss = 52831.94 - 18244.32 = 34587.62

You can only compare (add or subtract) different amount of money if they are in the
same spot on your time graph.

e.g. What is better , getting $500 today or getting $540 one year from now?
This is not a valid question, since we have to know what rate of interest is involved.

getting $500 today is not the same as getting $540 one year from now, if the rate is 6%
but would be the same if the rate is 8%

Answer 2

The answer to this question, thanks to Reiny hainy, is -$28,870.77.