When purchasing a home, which fixed mortgage is better to get, a 15 or 30 year? If you look at the total cost of the loan, a 15-year mortgage will always save you money, simple enough, right? However, if we want to see what the optimal mathematical answer is, we need to factor in what the credit score is, what the interest rate is, what the opportunity costs are, what the investment return is, and what the inflation rate is.

In this article, we will compare the 15 and 30-year mortgages over a 30-year time period. We will assume that we have an excellent credit score and we will own the house for the duration of the loan. (We could create many scenarios to compare the difference between these loans, but for this study, we will employ the full duration to illustrate the math most simply and clearly. The answer to other scenarios can most likely be intuited from the conclusions drawn in this article.)  To equate the total capital committed, we will invest the difference between the monthly payments into a portfolio that returns 10%, 8%, or 6%. For example, the 15-year loan will have a higher monthly payment, so for the first 15 years, that money will only go toward paying off the mortgage. The 30-year loan will have a lower monthly payment, so, during the first 15 years, we will invest the difference between the monthly payments of the 15-year loan and the 30-year loan. Then, at year 15, the 15-year loan will have been paid off, so we will begin to invest the monthly payment amount for the 30-year loan until year 30. All of these numbers will be inflation-adjusted, so when the 15-year loan starts investing in year 16, it will be doing so with inflation-adjusted dollars, meaning that it will be investing a lower amount than what the monthly difference says in year 1. This way, at the end of 30 years, we will have committed the same exact capital, and we will be able to see which mortgage was better mathematically when counting for inflation, which significantly affects the results. (Mortgages don’t adjust the monthly payment for inflation, so a $1000 monthly payment today is not the same as a $1000 monthly payment in year 20 if inflation has been present.) For all of the data you see in this article, the inflation rate was set to 3%, capital gains were 15%, and income tax was 20%.  All investment results were calculated using a Monte Carlo simulation that factored in both return and standard deviation. The table below displays the optimal way to choose a mortgage, and the rest of the article will explain how we arrived at these answers.

Only the 30-year rate is shown for simplicity. If you have an excellent credit score, 15-year rates are generally 50 basis points or .5% lower than 30-year rates. Thus, if the 30-year interest rate was 7%, the 15-year rate would be 6.5%, and you would choose the 15-year mortgage in all scenarios given the 6.3% + column on the chart.  If the 30 year rate 3.7% or below, you would choose the 30 year mortgage in all scenarios.

15 vs. 30 year In a High Interest Rate Environment

We will examine a $400,000 mortgage in a high-interest rate environment, as seen during 2023 and early 2024. The 15-year rate is 6.5%, and the 30-year is 7%. (High-interest rates relative to the last 20 years)

By choosing the 15-year mortgage, we will have a higher monthly payment, but we will save considerable money on interest.

To equate the two loans, we must invest the difference between the monthly payments. The 15-year loan doesn’t invest anything until it has been paid off, while the 30-year loan invests $823 per month for 15 years, and then it stops adding to the investment.

Putting it all together, with a 10% return, the 15-year- outperforms the 30-year results by almost $30k.  (For simplicity, we aren’t factoring in the home’s end market value, which is why the net result is negative.)

Now, let’s look at an 8% investment return. While the overall net result is worse for the 15 and 30-year mortgages, the 15-year outperformed the 30-year by even more. This is intuitive, as the lower the investment return, the more closely we approach the no-investing scenario, where the 15-year loan benefits from paying much less interest.

Lastly, here’s the same study with a 6% investment return. As mentioned, the lower the investment return, the more the 15-year mortgage outperforms.

When the 30-year rate is at 7% or higher, we can conclude that the 15-year loan is better than the 30-year loan with an investment return of 10% or below.  

But what would the answer be in a lower interest rate environment?

15 vs. 30 Year In a Low Interest Rate Environment

Now, we will look at a $400,000 loan at 2021’s average mortgage rate, 2.5% for the 15-year and 3% for the 30-year. Like 2024 interest rates, the 15-year loan will save us money on interest; however, it is not nearly as significant as before.

With the low interest rate and 10% investment return, the 30-year mortgage significantly outperformed the 15-year. The lower interest rates provided a much lower total loan cost, which allowed the investment account to outgrow the total mortgage cost. (This is largely due to inflation, as paying $1,686 per month in year 20 is not the same as paying $1,686 in year 1. Couple that with an investment account that is exceeding inflation, and you have the recipe for outperformance.)

With an 8% investment return, the 30-year mortgage is also an easy winner here.

Finally, here’s a 6% investment return. The 30-year is a winner here again, and as we saw before, the lower the investment return, the more the 15-year loan benefits due to the interest saved.  (Again, this should be intuitive as the investment account makes up for the extra interest cost of a 30-year loan.)

When the 30-year rate is at 3%, we can conclude that the 30-year loan is better than the 15-year loan with an expected annual investment return of 6% or more. 

Conclusion

When choosing a mortgage, be sure to factor everything in, as the correct result isn’t always what it appears to be at first glance.  Once again, here is the optimal way to choose a fixed mortgage term. 

James Di Virgilio

Author James Di Virgilio

More posts by James Di Virgilio