Final answer:
To find the total interest paid on a $85,000 loan at 7.50% for 30 years, calculate the monthly payment and multiply by the number of payments. Subtract the original loan amount from this total to get the interest.
Step-by-step explanation:
The total interest the Montgomerys will pay on a $85,000 loan at 7.50% interest for 30 years can be calculated using the formula for an amortized loan repayment.
First, calculate the monthly payment using the formula:
PMT = P x (i / (1 - (1 + i)^-n))
Where:
- PMT = monthly payment
- P = principal amount ($85,000)
- i = monthly interest rate (7.50% annual rate divided by 12 months)
- n = total number of payments (30 years x 12 months)
The monthly interest rate is 7.50% divided by 12, which is 0.625%.
Converting the percentage to a decimal, we have 0.00625. The number of payments over 30 years is 30 x 12, which equals 360 payments.
Next, substitute these values into the payment formula:
PMT = 85000 x (0.00625 / (1 - (1 + 0.00625)^-360))
This will give you the monthly payment. Multiplying the monthly payment by the number of payments (360) will give you the total amount repaid over the life of the loan.
Subtract the principal amount ($85,000) from this total to find the total interest paid.