Some Mortgage Payment Arithmetic

Relative to a 50-year mortgage

Suppose you take out a standard 30-year fixed-rate mortgage for $100,000 at a monthly interest rate of 0.5 percent (or 6 percent per year). The monthly payment for principal and interest is $599.55.

The first month’s interest is 0.5 percent of $100,000, which is $500. So your initial monthly payment reduces your outstanding balance by $99.55. Each month, you accrue slightly less interest and pay off more principal. After 360 payments, your outstanding balance is zero. The mortgage is paid off.

Suppose instead you take out a 50-year mortgage, also at a monthly interest rate of 0.5 percent. The monthly payment is now $526.40, which will result in the loan being paid off after 600 payments. Meanwhile, your first payment only reduces your outstanding principal by $26.40, and after 30 years you still have $73,480 of principal outstanding.

Over the years, lenders have come up with many gimmicks to lower the initial monthly payment on a mortgage. The 50-year mortgage is simply the latest gimmick. The result of any such gimmick is to slow down the rate of equity buildup, so that your outstanding balance stays higher for longer.

If interest rates remain stable, then a 50-year mortgage is equivalent to a mortgage with a monthly payment of $526.40 and a “balloon” payment of $73,480 due after 30 years. That sort of “balloon” mortgage would be one way to lower the monthly payment on a 30-year mortgage. But, again, there are many gimmicks that will do something similar.

Should you want to make the trade of having your equity build up more slowly in order to get a lower monthly payment? It probably makes sense if you see your income rising in the future. Whether your income is headed higher because of where you are in your career or because of general inflation, a lower monthly payment now will help you afford a house more in line with your future prospects.

I should point out that the main determinant of your true equity buildup will be the rate at which your house appreciates. If you buy at a good time and your home appreciates at 10 percent per year, your 6 percent mortgage is a bargain. If your home value goes down by 1 percent per year, your investment has turned out badly.

Some people will tell you that the sooner you pay off your mortgage, the more you save in interest payments. That is not proper financial analysis, because it does not take into account the opportunity cost of the money you use to pay off principal sooner.

Whether paying off a mortgage sooner helps you or hurts you depends on the alternative use of those funds. If you have a 6 percent mortgage, and you could invest funds at 7 percent, then don’t pay down the mortgage. If instead you would put those funds in a savings account that earns 4 percent, then paying off the mortgage is preferable.

For the more advanced financial analysis, you would take into account other factors, having to do with uncertainty. But we can leave those aside for now.