You plan to buy a car in one year. It will cost $15,000 at that time. You now have $5,000 in a bank that pays 12% compounded monthly. You will save for the car by making monthly deposits in the bank for the next 12 months. How much will you have to deposit each month to have enough money in total to make the purchase?
A)$738.50
B)$835.18
C)$769.43
D)$682.80

Question

Quizplus · Accepted Answer

First, we need to find how much the $5,000 will grow to in one year at 12% compounded monthly:

$5,000 x (1 + 0.12/12)^12 = $5,636.39

To reach a total of $15,000, we need to save an additional:

$15,000 - $5,636.39 = $9,363.61

Using the formula for the future value of an annuity:

FV = PMT x [(1 + r)^n - 1]/r

where FV is the future value, PMT is the monthly deposit, r is the monthly interest rate (0.12/12), and n is the number of periods (12), we can solve for PMT:

$9,363.61 = PMT x [(1 + 0.12/12)^12 - 1]/(0.12/12)

PMT = $738.50

Therefore, you need to deposit $738.50 per month to have enough money to buy the car in one year. Answer choice A is the best choice.

You Plan to Buy a Car in One Year