To find Jessica's monthly payment, we can use the formula for calculating the monthly payment on an amortized loan:
P = (r * A) / (1 - (1 + r)^(-n))
Where:
P is the monthly payment
r is the monthly interest rate (5.6% / 12)
A is the loan amount ($53,000)
n is the total number of payments (15 years * 12 months per year)
(a) Calculating the monthly payment:
r = 5.6% / 12 = 0.0467 (rounded to 4 decimal places)
n = 15 * 12 = 180
P = (0.0467 * 53000) / (1 - (1 + 0.0467)^(-180))
P ≈ $416.68
So, Jessica's monthly payment is approximately $416.68.
(b) To find the total amount repaid, we multiply the monthly payment by the total number of payments:
Total amount repaid = P * n
Total amount repaid ≈ $416.68 * 180
Total amount repaid ≈ $75,002.40
Therefore, Jessica's total amount to repay the loan is approximately $75,002.40.
(c) To find the total amount of interest paid, we subtract the loan amount from the total amount repaid:
Total interest paid = Total amount repaid - Loan amount
Total interest paid ≈ $75,002.40 - $53,000
Total interest paid ≈ $22,002.40
So, Jessica will pay approximately $22,002.40 in total interest over the term of the loan.