Final answer:
The finance charge for a $225,000 loan at 6.1% APR over 25 years is the total amount paid in payments over the term minus the original loan amount. To find this, calculate the monthly payment using the loan formula with the monthly interest rate and total number of payments, then multiply by the number of payments to get the total paid amount. The finance charge is this total minus $225,000.
Step-by-step explanation:
The finance charge for a $225,000 loan at 6.1% APR to be paid off in 25 years can be calculated using the formula for an amortizing loan. This formula incorporates the principal (P), the annual interest rate (r), and the total number of payments (n). The monthly payment (M) is found using the formula M = P[r(1+r)^n] / [(1+r)^n - 1]. For a loan with an APR, the interest rate used in the calculation is the monthly interest rate, which is the APR divided by 12 (the number of months in a year). After computing the monthly payment, calculating the total amount paid over the 25 years gives us the sum of all payments. The finance charge is then the total paid minus the original loan amount.
Let's calculate the monthly payment first:
- Convert APR to a monthly rate: 6.1% / 12 = 0.0050833
- Calculate total number of payments: 25 years * 12 months/year = 300 payments
- Use the formula to calculate the monthly payment: M = $225,000[0.0050833(1+0.0050833)^300] / [(1+0.0050833)^300 - 1]
- Once you have M, multiply by 300 to get the total amount paid over 25 years.
- Subtract the original loan amount from the total amount paid to find the finance charge.