An Analysis of the Interest Savings from Choosing a Shorter Amortization Period

Many financial planners and commentators make a great ballyhoo about the large amount of interest that can be saved by choosing a shorter mortgage amortization period. Their typical analysis goes as follows. (We will use monthly compounding rather than semiannual compounding to simplify the math.)

Suppose you obtain a $100,000 mortgage loan at 5.2% compounded monthly. The following table compares 20- and 25-year amortizations.

Amortization period	Monthly payment ($)	Total of all payments ($)	Total interest ($)
25 years	596.30	178,890	78,890
20 years	671.05	161,052	61,052
Difference:	(74.75)	17,838	17,838

By choosing a 20-year amortization, you will have interest savings of $17,838. The savings result from eliminating payments of $596.30 per month during Years 21 to 25 by spending an extra $74.75 per month during Years 1 to 20. That is,

Interest savings = (5 12 $596.30) ? (20 12 $74.75) = $17,838

It seems quite astoundingincreasing the monthly mortgage payment by a little more than 10% reduces the total interest costs by over 23%! The usual conclusion is that reduction of your mortgages amortization period should be one of your highest financial priorities because of the amazing interest savings. In the present example, you will be $17,838 ahead by choosing the 20-year amortization.

Do you see any flaws in this conventional analysis? Is it complete? Does it violate any basic concept you have learned? (Clearly, the analysis must be problematicotherwise, we would not be making an issue of it. But before reading on, cover up the remainder of the discussion and take five minutes to see if you can identify the error made by so many experts.)

The main flaw in the analysis is that a basic concept in financethe time value of moneyhas been ignored. Whenever you add nominal dollar amounts that are paid on different dates, you are ignoring the time value of money. The longer the time frame over which the payments are spread, the more serious the resulting error will be. In the preceding analysis, a dollar in Year 25 is treated as having the same value as a dollar in Year 1. In fact, individual dollars saved in Years 21 to 25 have, on average, significantly less economic value than extra dollars spent in Years 1 to 20.

Let us do a rigorous analysis to determine the amount of the economic advantage of the shorter amortization period.

QUESTIONS

1. For the first 20 years, the monthly payments on the 25-year amortization are $74.75 lower than the payments on the 20-year amortization loan. Suppose you invest this difference each month to earn the same rate of interest that you pay on either mortgage. How much will you accumulate after 20 years?

2. What will be the balance owed after 20 years on the 25-year mortgage? Compare this balance to the Question 1 result. Which mortgage alternative puts you in a better financial position 20 years from now? Where did all of the interest savings go?

3. How will the outcome differ if the rate of return on your investments is higher than the interest rate you pay on your mortgage?

4. Write a decision rule that your friends (who have not had the good fortune to take this course) can use to decide whether to select a longer or a shorter mortgage amortization period.