EXAMPLE 11 Paying Points

Suppose that you are offered a 30-year mortgage at 3.5% if you are willing to pay 2 points. What is the APR of the corresponding conventional loan, and what is its EAR?

The amount of the mortgage is not specified; in fact, to answer the question, we don’t need to know that. But to make the example concrete, suppose that the mortgage is for $100,000.

To have the full $100,000, you need to borrow $100,000/(1 - 0.02) — $102,041. To pay off that amount over 360 months at 3.5% annual interest, the payment can be found to be $458.21 from . We apply this payment to determine what interest rate it would correspond to in repaying a loan of only $100,00° by finding and we arrive at an APR of 3.663%. The corresponding EAR is