Final answer:
Amy will pay a total of $4,250 in interest over the life of the loan.
Step-by-step explanation:
To find the total amount of interest Amy will pay, we need to determine how long it will take her to repay the loan. The monthly payment of $250 will continue as long as necessary, followed by a smaller final payment. Let's calculate the number of months it will take to repay the loan:
We can use the formula for the present value of an annuity:
PV = PMT × [(1 - (1 + r)^(-n)) / r]
Where:
PV = Present value (loan amount) = $15,000
PMT = Monthly payment = $250
r = Monthly interest rate = 5.4% or 0.054
n = Number of months
Substituting the values into the formula, we can solve for n:
$15,000 = $250 × [(1 - (1 + 0.054)^(-n)) / 0.054]
Solving this equation, we find n ≈ 77.50. This means it will take approximately 77 months to completely repay the loan.
To calculate the total amount of interest, we can subtract the loan amount from the total payments:
Total Payments = Monthly Payments × Number of Months = $250 × 77 = $19,250
Total Interest = Total Payments - Loan Amount = $19,250 - $15,000 = $4,250
Amy will pay a total of $4,250 in interest over the life of the loan.