| So a common question when determing the right mortgage for you is “If I can afford the higher monthly payment on a 15-year mortgage, is it a better financial decision to take a 15-year mortgage or a 30-year mortgage?” |
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| Here is one way to look at this question… |
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| 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. |
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| 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. |
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| 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. |
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| 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. |
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| For example, if we invest at a reinvestment rate of 9 percent, the $200 per month from the 30-year mortgage cumulates to $79,330.49, which is exactly the outstanding liability on the 30-year mortgage at that point. On the other hand, the $1750 up front from the 15-year cumulates to $6716.58, and there is no outstanding liability. |
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| To summarize, with a 9 percent re-investment rate, we have after 15 years: |
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15-year mortgage |
30-year mortgage |
| investment proceeds |
$6716.58 |
$79,330.49 |
| mortgage balance |
0 |
$79,330.49 |
| Net |
$6716.58 |
$0.00 |
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| What this example shows is that if the re-investment rate equals the mortgage rate, then the financial difference between the loans boils down to the fact that the 15-year loan has a lower cost. This makes the 15-year the better choice. |
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| If the re-investment rate is lower than 9 percent, the case is even stronger for the 15-year mortgage, because the "net" for the 30-year mortgage is negative. If the reinvestment rate is much higher than 9 percent, then it is advantageous to have the lower monthly payment on the 30-year mortgage. The breakeven point is about 10.34 percent. If you believe that you can earn 10.34 percent or more on alternative investments, compared with a 9 percent mortgage rate, then a 30-year mortgage will leave you wealthier. |
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What about taxes? |
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| Many people have asked whether the tax deductibility of mortgage interest changes this analysis. One mistake people make is to compare a pre-tax reinvestment rate with an after-tax mortgage rate. The thought is that if you can earn 6 percent on an investment and pay 9 percent as a mortgage rate, if your tax rate is more than 33 percent you come out ahead. In fact, you will be taxed on your investment income, so both the re-investment rate and the mortgage rate should be adjusted for taxes. As a first approximation, taxes are a wash and do not change the above calculation. |
