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15-year versus 30-year Mortgages

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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?”
Here is one way to look at this question…
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.
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.
To summarize, with a 9 percent re-investment rate, we have after 15 years:
  15-year mortgage 30-year mortgage
investment proceeds $6716.58 $79,330.49
mortgage balance 0 $79,330.49
Net $6716.58 $0.00
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.
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.

What about taxes?

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.
 
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