How much interest is paid in the 53rd monthly payment interval of a loan for $43 200? The loan is amortized at a rate of 9.17% compounded annually over 7 years.

Question

Quizplus · Accepted Answer

First, we need to find the monthly interest rate by dividing the annual rate by 12:

9.17% / 12 = 0.7642%

Next, we need to find the total number of payments over the life of the loan (7 years = 84 months). Since we want to find the interest paid in the 53rd month, we can use that as the n value in the formula for the total amount of the loan:

PV = A * ((1 - (1 + r)^(-n)) / r)

Where:
PV = present value of the loan ($43,200)
A = the monthly payment
r = the monthly interest rate (0.7642%)
n = total number of payments (84)

Solving for A:

A = PV / ((1 - (1 + r)^(-n)) / r)

A = $612.75

Now we can find the interest paid in the 53rd month by subtracting the principal portion of the payment from the total payment:

Interest = Total payment - Principal portion

To find the principal portion, we can use the formula:

Principal = A * (1 - (1 + r)^(-x)) / r

Where x is the number of payments made (52) and r and A are the same as before.

Principal = $447.64

Total payment = $612.75

Interest = $612.75 - $447.64

Interest = $165.11

Therefore, the answer is C) $144.11 (rounded to the nearest cent).

How Much Interest Is Paid in the 53rd Monthly Payment