Question

You'd like to buy a new sports car. You're considering borrowing $10,323 in order to purchase the car. You'll borrow money from Bank ZoomZoom at an APR of 9%. Bank ZoomZoom compounds interest monthly. You've decided to structure the loan so that payment shrink each month by -2% per month. The first payment will be made immediately. You'll make a total of 79 monthly payments. Determine the size of the 17th monthly payment.

Answer 1

To determine the size of the 17th monthly payment, first calculate the monthly payment amount for the loan using the given information. Then, find the 17th monthly payment by decreasing the previous month's payment by 2%. The size of the 17th monthly payment is approximately $136.40.

Step-by-step explanation:

To determine the size of the 17th monthly payment, we need to calculate the monthly payment amount for the loan.

First, we need to find the monthly interest rate by dividing the annual interest rate by 12 (since the interest is compounded monthly). So, the monthly interest rate is 9% / 12 = 0.75%.

Next, we can use the loan formula:

Monthly Payment = (Principal * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate) ^ -Number of Payments)

Substituting the values, we have:

Principal = $10,323

Monthly Interest Rate = 0.75%

Number of Payments = 79

Plugging these values into the formula, we can calculate the monthly payment amount, which is approximately $139.19.

Since the payment shrinks by -2% per month, we need to calculate the 17th monthly payment, which is 2% less than the previous month's payment:

17th Monthly Payment = 16th Monthly Payment - (2% * 16th Monthly Payment)

Substituting the value, we get:

17th Monthly Payment = $139.19 - (2% * $139.19) ≈ $136.40.