Final answer:
To find the highest APR a student can afford for a $3,600 loan with a monthly payment limit of $110 over 36 months, an equation involving the installment loan monthly payment formula must be used.
Step-by-step explanation:
To determine the highest APR rate a student can afford when borrowing $3,600 over 36 months with a monthly payment limit of $110, we need to use the formula for the monthly payment on an installment loan which considers the loan amount, the interest rate, and the number of payments:
M = P * (i(1+i)^n) / ((1+i)^n - 1) where: M = monthly payment, P = principal amount (loan amount), i = monthly interest rate (APR/12), n = total number of payments. Here, P = $3,600, M = $110, and n = 36. We need to find the highest APR that can be afforded, so we can rearrange the formula to solve for i, which represents the monthly interest rate.
However, you can use an iterative process to approximate the monthly interest rate (and thus the APR) by plugging in different interest rates until the monthly payment closely matches the limit of $110.