Now to give you a sense of how these factors interact consider the following three mortgage scenarios and use them to calculate APR or EIR and AEY.

Mortgage1 has 6% fixed coupon rate, no points, no fees, 30-year amortization and expected life of three years.

Mortgage2 has 4.5% coupon rate, 2 points, 2% origination fees, 2% prepayment penalty if prepaid within the first 5 years, 30-year amortization and expected life of three years.

Mortgage3 is the same as mortgage2, except that it is uncertain how long the household (the borrower) will stay in the house before moving and prepaying the loan. But you estimate that there is 90% probability that the borrower will sell the house and move at the end of 10th year and so there is a 10% chance that the borrower will hold the mortgage till the end of amortization period. Prepayment penalty is typically a percentage of the amount being prepared.

Now for each of the three mortgage scenarios calculate the APR or EIR, and the annualized effective yield (AEY)