Final answer:
The total interest owed on an amortized loan can be calculated by subtracting the principal amount from the total payment. To find the total payment, we first calculate the fixed monthly payment using the formula for the fixed monthly payment. Then, we multiply the fixed monthly payment by the total number of monthly payments to find the total payment. Finally, subtract the principal amount from the total payment to find the total interest owed.
Step-by-step explanation:
To calculate the total interest owed on an amortized loan, we need to use the formula:
Total Interest = Total Payment - Principal Amount
First, we need to calculate the total payment using the formula for the fixed monthly payment:
PMT = P * r * (1 + r)^n / ((1 + r)^n - 1)
Where:
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- PMT = fixed monthly payment
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- P = principal amount of the loan ($45,000)
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- r = monthly interest rate (7.6% / 12 = 0.00633)
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- n = total number of monthly payments (9 years * 12 months = 108)
Once we calculate the fixed monthly payment, we can use it to calculate the total payment by multiplying it by the total number of monthly payments:
Total Payment = PMT * n
Finally, we can calculate the total interest owed by subtracting the principal amount from the total payment:
Total Interest = Total Payment - Principal Amount
Plugging in the values, we get:
PMT = 45000 * 0.00633 * (1 + 0.00633)^108 / ((1 + 0.00633)^108 - 1) ≈ $594.87
Total Payment = $594.87 * 108 ≈ $64,312.59
Total Interest = $64,312.59 - $45,000 ≈ $19,312.59