A student loan is taken out for $8,500 at 6.6%. The student graduates 2 years and 3 months after the
Loan is acquired. Payments are deferred for 6 months after graduation. Find the the monthly
Payment. Assume 30-day months and that the term of the loan is 10 years.

Question

Quizplus · Accepted Answer

First, calculate the total time from when the loan is taken out until payments start: 2 years and 3 months plus an additional 6 months of deferment equals 2 years and 9 months, or 33 months. However, this period only affects the accumulation of interest if it is not capitalized, and the problem does not specify this detail. Assuming a standard student loan with a 10-year (120 months) repayment period, we use the formula for a fixed-rate loan payment. The monthly interest rate is 6.6% annually, or 0.55% monthly (6.6% divided by 12). Using the formula for an installment loan: P = [rPV] / [1 - (1 + r)^-n], where P = payment, r = monthly interest rate (as a decimal), PV = present value (loan amount), and n = number of payments. Plugging in the values: r = 0.066 / 12, PV = $8,500, n = 120, we find P ≈ $114.34.

A Student Loan Is Taken Out for $8,500 at 6