11.23 A Few Thoughts about Mortgages

There are a few key points regarding mortgages, which require summary and notice. 

1. Interest payments are tax deductible. Tax deductibility is important simply because it reduces the after-tax cost of the mortgage. Funds that would otherwise have gone to pay tax instead go to debt service. This benefit is reduced as the interest portion of the mortgage payment is reduced with time. 
2. Partway through the loan, half the loan will have been paid off. A mortgage has a kind of “half-life.” In the foregoing example, half the loan will have been paid off after six years. This half-life will be greater than half the length of the mortgage because initially the annuity payments are used mainly to pay interest on the loan! 
3. Total interest paid may be much greater than and in longer-term cases, a multiple of the principal – this can be calculated by evaluating the total payments minus the principal. 

In the foregoing example, over the ten years the borrower will have paid a total of 10 annual payments of $15,576.32 for a total of $155,763.20. If you subtract from this figure the loan principal of $100,000, you are left with a figure of $55,763.20, which represents the total amount of interest paid over the life of the mortgage (unadjusted for time value). In other words, interest paid represents an additional 55% approximately of the principal borrowed. (We take note again that most mortgages require monthly payments and that, in today’s marketplace, most mortgages are 15 to 30 years.)

Let us compare 15- and 30-year mortgages in terms of the ratio of interest payments made relative to the principal. We remind ourselves that in the above instance (10 years and 9%) we had 55% interest payments relative to the loan principal. Let us use $100,000 of principal again, and, this time, 6% in interest. We shall again employ the formula:  

Principal ÷ PV Annuity Factor = Periodic Payment 

15 years:      ($100,000) ÷ (9.7122) = $10,296.33 

Over 15 years total payments will equal (15) ($10,296.33) = $154,444.95. In this case, interest payments will equal 54.44% of the principal. 

30 years:      ($100,000) ÷ (13.7648) = $7,264.91 

Over 30 years, total payments will equal (30) ($7,264.91) = $217,947.30. In this case, interest payments will equal 117.95% of the principal. 

Even though the annual payments are less in the 30-year case, we see that interest payments multiply enormously over time.