Final answer:
Approximately $125.29 of the first payment on a $6,500 installment loan with a 5.5% annual interest rate and $155 monthly payments will go to the principal after subtracting the interest portion of the first payment.
Step-by-step explanation:
The first payment:
To calculate how much of the first payment on an installment loan will go toward the principal, we need to determine the amount of interest that is part of the first payment. The interest for the first payment is calculated using the formula for simple interest: Interest = Principal × rate × time.
For a loan with a principal of $6,500, an annual interest rate of 5.5% (or 0.055 when expressed as a decimal), and a monthly payment cycle, the interest for the first month is calculated as follows: Interest = Principal × monthly interest rate × time = $6,500 × (0.055 ÷ 12) × 1 = $29.71 approximately The monthly payment is $155. Therefore, the amount toward the principal is: Principal portion = Monthly payment - Interest = $155 - $29.71 = $125.29 approximately So, $125.29 of the first payment will go toward reducing the principal balance of the loan.