You want to purchase a car for $40,000 when you graduate in two years. At that time you will take out a 5-year bank loan at 12% compounded monthly. Based on your estimated earnings, you think you'll be able to afford loan payments of $750 per month. You plan to save up the difference between the cost of the car and the amount you'll borrow by making quarterly deposits over the next two years in a bank account that pays 8% compounded quarterly. How large must those deposits be? (Round to the nearest dollar)
A)$523
B)$637
C)$732
D)$845

Question

Quizplus · Accepted Answer

First, we need to calculate the amount we will need to borrow from the bank.

$40,000 car cost - (2 years x 4 quarters per year x $deposit amount x 1.02^8) = $Borrowed

Using the formula for the future value of an annuity, we can solve for the deposit amount:

$40,000 - ($deposit amount x 1.02^8 - 1) / 0.02 = $Borrowed

$750 loan payment x 12 months per year x 5 years = $45,000

$Borrowed = $45,000 / (1 + 0.01)^60 = $27,699

$40,000 - (2 x 4 x $deposit amount x 1.02^8) = $27,699

$deposit amount = $732 (rounded to the nearest dollar)

Therefore, choice C is the best answer.

You Want to Purchase a Car for $40,000 When You