To calculate the monthly payment, we can use the formula for a fixed-payment loan:
P = (Pv * r) / (1 - (1 + r)^(-n))
Where:
Pv = present value of the loan
r = monthly interest rate
n = total number of payments
P = fixed monthly payment
a. To find the monthly payment, we need to first calculate the monthly interest rate and total number of payments:
Monthly interest rate = APR / 12 = 0.12 / 12 = 0.01
Total number of payments = 15 years * 12 months/year = 180
Plugging these values into the formula, we get:
P = (25000 * 0.01) / (1 - (1 + 0.01)^(-180)) = $285.41 per month
Therefore, the monthly payment is $285.41.
b. To determine the total amount paid over the term of the loan, we can simply multiply the monthly payment by the total number of payments:
Total amount paid = monthly payment * total number of payments
Total amount paid = $285.41 * 180 = $51,373.80
Therefore, the total amount paid over the term of the loan is $51,373.80.
c. To find the percentage of the total amount paid that is applied toward the principal and interest, we can use the amortization schedule. An amortization schedule breaks down each payment into its principal and interest components. Using a loan calculator or spreadsheet, we can generate the following schedule: in file attachment
From the table in file attachment, we can see that the total principal paid over the term of the loan is $25,000 (the initial loan amount) plus $281.12, or $25,281.12. To find the percentage of the total amount paid that is applied toward the principal, we can divide the total principal by the total amount paid and multiply by 100:
Percentage of total amount paid applied toward principal = (Total principal / Total amount paid) * 100
Percentage of total amount paid applied toward principal = ($25,281.12 / $51,373.80) * 100 = 49.20%
Therefore, 49.20% of the total amount paid is applied toward the principal, while the remaining 50.80% is paid for interest.