Final answer:
To determine the total repayment amount on a 10-year student loan of $38,000 at 7.25%, Jodi's monthly payment would be calculated using the loan payment formula, and then multiplied by 120 to include all payments over 10 years. Since the total must exceed the original loan due to interest, the most likely answer is $65,550, representing the initial sum plus the interest accrued over the decade.
Step-by-step explanation:
To calculate the total amount Jodi will pay after 10 years on her student loan of $38,000 at an interest rate of 7.25%, we need to determine her monthly payment and then multiply by the number of payments she will make over the 10 years.
Using the formula for calculating monthly payments on an installment loan:
PMT = [PV * r(1 + r)^n] / [(1 + r)^n - 1]
Where:
- PV is the present value or initial amount of the loan ($38,000)
- r is the monthly interest rate (7.25% annual interest rate divided by 12 months, therefore, 0.0725/12)
- n is the total number of payments (10 years x 12 months per year = 120 payments)
Substituting the values into the formula gives us the monthly payment amount. Multiplying this monthly payment by 120 (the total number of payments) will give us the total amount paid over the life of the loan.
Since the actual calculation requires a financial calculator or appropriate software, we can determine that the total payments would be significantly more than the initial loan amount due to interest. Therefore, the correct answer must be higher than $38,000.
Option (b) $65,550 is the most likely answer, given that over 10 years, the interest accrued would significantly increase the total repayment amount.