The interest rate is higher on 30-year mortgages than on 15-year mortgages. This can show up as a higher rate, more points, or both. Often, one can obtain 15-year and 30-year fixed-rate mortgages at identical rates but with 1 - 3 more points up front for the 30-year. A typical differential is 1-3/4 points up front.
Suppose we compare the 15-year to the 30-year as follows: We take out a $100,000 mortgage at 9 percent in either case. However, with the 15-year, because we pay 1.75 points less up front, we have $1750 to invest.
The monthly payment on the 30-year mortgage is only $804.62, compared with $1014.27 for the 15-year. Therefore, each month, we have over $200 more available to invest with the 30-year mortgage.
What we are going to do is invest the money ($1750 up front in the case of the 15-year, $200+ per month in the case of the 30-year) at a reinvestment rate until we have reached the end of 15 years. At that point, we will compare the value of what we have invested to our outstanding liabilities.