Answer:
Explanation:
To find Nicole's monthly payment, total amount to repay the loan, and total amount of interest she will pay, we can use the formula for calculating the monthly payment on an amortized loan:
Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Payments))
(a) Finding Nicole's monthly payment:
Loan Amount = $22,500
Annual Interest Rate = 7.75% = 0.0775 (converted to decimal)
Monthly Interest Rate = Annual Interest Rate / 12 = 0.0775 / 12
Number of Payments = 3 years * 12 months/year = 36
Plugging in the values into the formula:
Monthly Payment = ($22,500 * (0.0775 / 12)) / (1 - (1 + (0.0775 / 12))^(-36))
(b) Finding the total amount to repay the loan:
Total Payment = Monthly Payment * Number of Payments
(c) Finding the total amount of interest Nicole will pay:
Total Interest = Total Payment - Loan Amount
Let's calculate the values:
(a) Monthly Payment:
Plugging in the values into the formula, we get:
Monthly Payment ≈ $717.38 (rounded to the nearest cent)
(b) Total Payment:
Total Payment = $717.38 * 36 = $25,823.68 (rounded to the nearest cent)
(c) Total Interest:
Total Interest = $25,823.68 - $22,500 = $3,323.68 (rounded to the nearest cent)
Therefore, the results are as follows:
(a) Nicole's monthly payment is approximately $717.38.
(b) If Nicole pays the monthly payment each month for the full term, her total amount to repay the loan will be approximately $25,823.68.
(c) If Nicole pays the monthly payment each month for the full term, the total amount of interest she will pay will be approximately $3,323.68.