Question

A home improvement loan is to be repaid by equal monthly payments for six years. The interest rate is 5.4% compounded monthly and the amount borrowed is $33,500. How much interest will the borrower pay over the six years?

Answer 1

To calculate the total interest paid on a home improvement loan with the given parameters, the monthly payment amount must first be calculated using the annuity formula, then this payment is multiplied by the number of payments to find the total paid, from which the original loan principal is subtracted to determine the total interest.

Step-by-step explanation:

To answer the question regarding the interest paid over six years for a home improvement loan of $33,500 at a 5.4% interest rate compounded monthly, one would typically use the formula for an annuity to determine the monthly payment and then calculate the total interest paid. Since the question seeks only the total interest, assuming one knows the monthly payment amount, the calculation would involve determining the total amount paid over the term of the loan and subtracting the principal amount from this total.

Without the specifics of the monthly repayment amount within the question's body, it is essential to start by finding this monthly payment using the formula for an annuity. This formula considers the principal loan amount, the monthly interest rate, and the total number of payments.

To calculate monthly interest, you divide the annual rate by 12 (5.4% / 12 = 0.45% per month). Over the course of six years, there will be 72 payments (6 years * 12 months). Subsequently, one would apply the annuity formula to find the monthly payment:
Monthly Payment = P [i(1 + i)^n] / [(1 + i)^n - 1] where P is the principal, i is the monthly interest rate in decimal form, and n is the number of payments.

After determining the monthly payment, multiply it by 72 to find the total amount paid over the life of the loan. Subtract the principal of $33,500 from this total to find the amount of interest paid.

The details provided in the example within the question, such as Joanna's house loan scenario, indicate how to use the annuity formula to calculate loan affordability and total payment, which are related concepts to the student's question about interest payment over the life of a loan.