Final answer:
The APR for a $2,000 student loan paid over 48 months with monthly installments of $49.30 can be estimated by comparing the total of the payments to the original loan amount and understanding that the APR takes into account the reducing balance over the term of the loan.
Step-by-step explanation:
To determine the APR of the student loan, we need to find the interest rate that would lead to monthly payments of $49.30 for a loan amount of $2,000 over 48 months. Calculating APR could involve complex financial formulas or using a financial calculator or software that performs iterative calculations to solve for the interest rate.
Without the exact calculation method available here, we can estimate the APR by considering the total payments made over the life of the loan which amounts to $49.30 × 48 months = $2,366.40, and comparing this with the original loan amount of $2,000. The difference, $366.40, represents the total interest paid over the life of the loan.
Understanding an accurate APR involves recognizing that it will be higher than just the simple interest rate of dividing total interest by the loan amount, because it also accounts for how the loan is paid down over time. In a typical APR calculation, monthly interest is applied to a gradually reducing principal amount, meaning each payment partially goes towards paying off interest and partially towards reducing the original loan amount. Financial formulas or calculators take this into account when calculating the APR.