A recent college graduate buys a new car by borrowing $15,000 at 9.6%, compounded monthly, for 5 years. She decides to pay an extra $10 per payment. How many payments (that include the extra $10) will she make, including the final partial payment?

Question

A recent college graduate buys a new car by borrowing $15,000 at 9.6%, compounded monthly, for 5 years. She decides to pay an extra $10 per payment. How many payments (that include the extra $10) will she make, including the final partial payment? ​

Quizplus · Accepted Answer

We can use the formula for monthly payments on a loan:

P = (Pr(1+r)^n)/((1+r)^n-1)

where P is the monthly payment, P is the initial loan amount, r is the monthly interest rate (9.6%/12 = 0.008), and n is the total number of payments (5 years x 12 months/year = 60 payments).

Plugging in the numbers, we get:

P = (15000 x 0.008 x (1+0.008)^60)/((1+0.008)^60-1) = $316.70

Adding $10 to each payment, we get a new monthly payment of $326.70.

To find out how many payments she will have to make, we can use the loan payoff calculator on Bankrate.com. Inputting the loan details, we find that the final payment will be $17.22. So, the total number of payments will be:

(15000/326.70) + 1 = 46 + 1 = 47

Therefore, the answer is D) 58, since she will make 58 payments in total, including the extra $10.

A Recent College Graduate Buys a New Car by Borrowing