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amy borrows $15,000 and will repay the loan with monthly payments of $250 as long as necessary, followed by a smaller payment. the first payment is due at the end of the first month and the nominal interest rate convertible monthly is 5.4%. what is the total amount of interest amy will pay?

User Wsams
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2 Answers

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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.

User Chasmani
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1 vote

Amy will make approximately 77.35 monthly payments of $250 to repay the loan. The total amount of interest Amy will pay is approximately $4,337.50.

Amy borrowed $15,000 with monthly payments of $250 and a monthly interest rate of 5.4%.

The number of months it will take to repay the loan using the present value of an annuity formula:

PV = PMT × ( ( 1 − ( 1 + r ) − n ) / r )

n ≈ 77.35. So, it will take approximately 77.35 months to repay the loan.

The total payments, we multiply the monthly payment amount by the number of months:

Total payments = Monthly payment × Number of months = $250 × 77.35 ≈ $19,337.50.

The total interest, we subtract the loan amount from the total payments:

Total interest = Total payments - Loan amount = $19,337.50 - $15,000 = $4,337.50.

User Zambezi
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