EXAMPLE 10 Your Federal Student Loan

We can do a similar analysis for a federal student loan. For such a loan, in effect you pay 1.073% interest in advance as a “loan origination fee” and then have a conventional loan for the principal at a set interest rate of 4.29%. For simplicity, we assume that you make the monthly interest payments until your repayment starts.

So suppose you need $10,000. You need to borrow . To pay off the $10,108.46 loan over 120 months, your payment, either from the amortization payment formula or from , is $103.74.

Although you are paying back as if the loan were for $10,108.46, you got only $10,000. We can use a spreadsheet to calculate the APR for a corresponding no-fee loan as in Example 9 above via ) and arrive at 4.521%.

The effective annual rate (EAR) of the corresponding no-fee loan is