EXAMPLE 4 Repaying Your Student Loan

The standard repayment option for federal direct student loans is repayment over 10 years with a minimum monthly payment of $50 at the end of each month, beginning six months after you graduate, and a minimum monthly payment of $50. For the $5500 student loan of Example 1 (page 910), if you didn’t pay the interest over the 51 months, what will your monthly payments be on the $6502.83 that you will owe at the start of repayment?

With the amortization payment formula, it’s easy to figure out your monthly payment. We have , monthly interest rate , and months for the payback. We find the payment as

So your monthly payment will be $66.74. (That is for this loan; you may owe still more per month for loans for your other years in college.) Hence, over the lifetime of the loan, you will pay almost . We say “almost,” because your last payment will differ by a few cents. Of the total, is interest during the 10-year payback period, plus the $ 1002.83 interest accrued during the deferment and grace periods (calculated in Example 1), for a total of $2508.80 in interest, on an original loan principal of $5500.

In fact, the amount you receive is reduced by an origination fee of 1.073% of the loan amount, or ; so altogether, you will pay almost 50% as much in interest and fees as the original principal. If you were to stretch your payments over more years (permissible in some circumstances), an even greater proportion would be interest.

You can check these amounts, and those for your own loans, at studentloans.gov/ myDirectLoan/mobile/repayment/repaymentEstimator.action and (with more options and details) at www.finaid.org/calculators/loandiscountanalyzer.phtml.