15 vs 30 Year Mortgages: What the Math Says

Author: Chris Talley

Published: March 6, 2021

Last updated: July 6, 2021

Introduction

In this post, we will take a mathematical approach to comparing 15 year mortgages against 30 year mortgages. The findings will challenge the general knowledge that is pervasive in the personal finance community, and will ultimately show that each type of mortgage is preferable in certain circumstances, even when one is guaranteed that cash invested in the market will earn returns above the loans' interest rates.

Scenarios

For this comparison, we have pulled 2 loans from bankrate.com for a home purchase of $500,000, with a 20% down payment.

The loan details are as follows:

We will assume that the home buyer who opts for the 30-year mortgage will be investing their $960.77 monthly savings into a broad-market index fund.

Considerations

As we follow the two consumers with these loans through time, we will be looking at the total amount of money they keep, up to that date. It is important to remember that, because the consumer with the 30-year mortgage is investing their monthly savings in the market, each time we compare the two, they will have both paid out the same total amount of money to date.

The question we will be asking at each time interval is “How much money did each homeowner keep?”

“Money that they keep” will be broken into three buckets:

1. Principal paydown: The money that has gone towards paying down the loan.
2. Tax refund: We will assume that each home buyer is deducting their mortgage interest, and has a marginal tax rate of 30%. This essentially means that the IRS is refunding them for 30% of the amount they pay towards interest.
3. Outside investments: The consumer with the 30-year mortgage will be investing $960.77 each month into outside investments. The 15-year borrower will be investing $0 until they have paid off their loan. After paying off their loan, they will invest all $2,630.34 of their previous monthly payment budget into index funds

The total amount of money they keep will be the sum of these three buckets.

Part 1: Using a fixed 8% return rate on outside investments

For simplicity, I will initially assume that the outside investments are in an index fund which returns a consistent 8% annual return for now, but I will revisit this assumption later in this post and replace it with a more rigorous approach using historical averages.

Now, let’s check in with them 1 month after the home purchase.

1-Month Checkin

After 1 month, let’s see where each homeowner’s money has gone:

We can see that after the first month, the 15-year borrower is ahead. This is because they are paying less interest than the 30-year borrower, and also because the 30-year borrower’s outside investments have not yet had any time to grow.

Now, the question is: if the 30-year borrower is counting on the growth of their outside investments to make up for the higher interest, then how long will it take for them to actually surpass the 15-year borrower?

Let’s see how things look after 1 year

1-Year Checkin

After 1 year, the totals are as follows

So we can see that even after 1 year, the 15-year borrower is still ahead of the 30-year borrower by approximately 6%

This means that after the first year, the 15-year borrower still has a higher net worth than the 30-year borrower, even accounting for the 8% annual return rate on the 30-year borrower’s outside investments.

🚨 First crucial note: If these homeowners end up selling the home after the first year, then the 15-year borrower will stay ahead. They will be cashing out their home equity, at which time they have the option to put that money into the same index funds that earn 8% per year. If this happens, the 30-year borrower will never catch up. In this scenario, the 15-year loan is better for growing wealth than the 30-year loan!

Breakeven point

Assuming they do not sell, how long will it take for the 30-year borrower’s market returns to finally cause them to surpass the 15-year borrower’s net worth?

Using the Rational Riches mortgage comparison calculator, we can see that this happens at the 4 year, 6 month mark.

This means that if the homeowners plan to sell before the 4 year and 6 month mark, then the 15-year mortgage will be preferable for building wealth. After that, the 30-year loan produces more favorable results.

Longer Time Horizon

Keep in mind that if the homeowners do not sell or cash out their home equity for a very long time, then the 30-year borrower does come out significantly ahead. Let’s do one final check-in after 30 years:

After 30 years, we can see that the 30-year mortgage has put the homeowner ahead by $506,384 or about 39%.

Conclusion 1

From this analysis, we can see that the 15 vs 30 year mortgage comparison is highly dependent upon the borrower’s time horizon for the loan. If planning to liquidate your equity in the home before the 30-year mortgage’s total surpasses that of the 15-year mortgage, then the 15-year mortgage provides better returns.

🚨 Second crucial note: Recognize that the 15-year mortgage is providing guaranteed interest savings, where the 30-year mortgage is providing more volatile market returns. The above numbers are not risk-adjusted, and thus are actually under-valuing the 15-year mortgage on a risk-adjusted basis. Additionally, they are considering the pre-tax value of the outside investments. Adjusting for long-term capital gains taxes would also make the 30-year mortgage less attractive.

Part 2: Using Historical Market Returns Instead of 8%

The above analysis assumed a consistent 8% annual return on outside investments. However, this is clearly not the case in the real world. Let’s now use historical market returns instead of a fixed return rate.

For this, I’ll use the Rational Riches mortgage comparison calculator’s “Use historical S&P 500 returns” feature. This feature allows us to compare loans against each other, while modeling our outside investments’ growth following historical S&P 500 returns starting on a given month of our choice.

So using the two loans above, and replacing our fixed 8% return rate with historical S&P 500 returns starting April of 1970, we can see that the two loans play out as follows:

In this scenario, we can see that 30 years after originating these loans, choosing the 30-year mortgage results in a nearly $4,000,000 benefit compared to the 15-year loan!

But this selection of April, 1970 seems arbitrary -- it’s just one random month in history. So next, I wrote a script which runs this same analysis repeatedly, starting in every month from January 1900 to December of 1990 and computes the average “benefit” historically of the 30-year loan compared to the 15 year loan.

The results:

• There is not a single month ever in this 90-year time period in which, after a 30-year time horizon, the 30-year mortgage underperforms the 15-year mortgage from a net worth perspective.
• The average benefit of the 30-year mortgage is $1,255,401
• The median benefit of the 30-year mortgage is $924,486
• The best benefit is the example I showed above -- using a start month of April, 1970, we see a benefit of $3,937,845
• The worst benefit of the 30-year mortgage was $200,358. And this is if we use S&P500 returns starting on June, 1902
• 75% of the time, we see a benefit of $539,644 or more
• 90% of the time, we see a benefit of $424,228 or more

The above numbers are for a 30-year time horizon. However, as I demonstrated in part 1 of this post, we should expect shorter time horizons to produce very different results. So I ran the same analysis for all time horizons from 1 to 30 years, and the results confirm our findings in part 1.

With a time horizon of 1 year, the 30-year loan outperforms the 15-year loan only 13.9% of the time.

You can see the full findings in this spreadsheet

Conclusions

As we can see, the 30- vs 15-year mortgage comparison is much more nuanced than many folks in the financial community portray. Even without adjusting for risk, if you plan to hold the home for a fairly short period of time, then a 15-year mortgage is likely to be a more effective wealth-growing tool.

However, if you plan to stay in the home and not cash out for 5 years or longer, then the 30-year mortgage is more likely to be the most effective wealth-building option. Whether that higher net worth is worth the potential added stress of holding a mortgage for twice as long, is something that each individual homeowner must assess for themself, and is a highly personalized decision.

⚠️ You can view the full findings in this spreadsheet

FAQ's

Q: Are these numbers inflation adjusted?

A: No, they are not. Keep in mind that adjusting for inflation would not change the comparison/ranking, but only the magnitude of the result

Q: Am I accounting for capital gains tax on the outside investments?

A: Not currently. If this is something that folks would like to see, let me know in the comments below!

Q: Why don’t we account for property appreciation in the net worth numbers?

A: The goal of this article and the calculator is to compare mortgages. Therefore, we only look at the components that will differ depending on the mortgage you choose. Home appreciation is not affected by the mortgage you choose. The one case where this might not be true is if, because of the lower payment, you would be comfortable buying a more expensive home on a 30-year mortgage than on a 15-year mortgage. But for the purpose of this comparison, we are assuming that the home you buy and when you sell it are factors that will not be influenced by the loan that you choose.

Q: Why don’t we account for property tax, insurance, and closing costs?

A: Similar to the answer directly above -- these don’t change with different loans, so they do not affect the comparison between the loans.

Q: Why did the historical analysis only go until 1990?

A: Because we are looking at a time horizon of up to 30 years, we need to have 30 years of market data after the start time of the loan. This post is being written in Feb 2021, using a data source which was last updated with historical market data through the end of 2020.

Q: Do the market returns include dividends?

A: Yes, the market returns include dividends, and assume dividends are reinvested. (source)