Question

Gary took out a 6-year car loan for $18,800 to be paid back with monthly payments at a 13.2% APR, compounded monthly. The loan offers no payments for the first 18 months. Gary is wondering how much he will pay in interest on the loan. Help him figure out the answer.

Answer 1

Gary will pay a total of $12,028.64 in interest on the car loan.

Step-by-step explanation:

To calculate the interest on the car loan, we first need to calculate the monthly payment amount. We can use the formula:

PMT = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where PMT is the monthly payment, P is the principal loan amount, r is the monthly interest rate, and n is the number of payments. In this case, P = $18,800, r = 0.132 / 12 (monthly interest rate), and n = 6 * 12 = 72 (total number of payments).

Once we have the monthly payment amount, we can calculate the total interest paid by multiplying the monthly payment by the number of payments and subtracting the principal loan amount.

Therefore, Gary will pay a total of $12,028.64 in interest on the loan.

Answer 2

$22,891.73

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 13.2/100

r = 0.132 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 18,800.00(1 + 0.132/12)(12)(1.5)

A = 18,800.00(1 + 0.011)(18)

A = $22,891.73

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $18,800.00 at a rate of 13.2% per year compounded 12 times per year over 1.5 years is $22,891.73.