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Two scenarios-

  1. 15-year fixed-rate mortgage. After 15 years (the mortgage is paid off) the monthly mortgage amount is invested into an S&P 500 index fund for 15 years.

  2. 30-year fixed-rate mortgage. Invest the difference between the 15 and 30 year mortgage into an S&P 500 index fund for 30 years (life of the mortgage).

What is the net worth after 30 years for both scenarios?

I've seen a 15-year comparison, but not 30:

Assumptions:

  • Mortgage Amount: $240,000 (home value 300k, 20% down)
  • 15 year APR: 2.852%
  • 30 year APR: 3.568%
  • Linear S&P 500 index fund growth: 4% (conservative)*
  • Long term capital gains: 15% (taken once at year 30)
  • With the standard deduction increased through Tax Cuts and Jobs, the mortgage interest will not be itemized.

Mortgage rates as of July 13th, 2020 from https://www.bankofamerica.com/mortgage/mortgage-rates/

*The 4% is an attempt to simplify the risk and variability of the market. According to http://www.moneychimp.com/features/market_cagr.htm, the historic annualized return (including dividends and inflation) is 7% for over 100 years.

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  • 2
    Good question - a nice answer would discuss the impact of increased overall leveraging with a 30 year mortgage [both the pros and cons], the impact felt by changing the assumed return of investments, and diversification of portfolio investments with a 30 year mortgage vs 'only owning' a home for the first 15 years in the 15 year mortgage [including the impact of potentially needing to move when the real estate market is up down or sideways]. – Grade 'Eh' Bacon Jul 13 '20 at 15:41
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    Also linear index fund growth (even at 4%) is not realistic - any investment that earns more than risk-free rates is going to have risk (fluctuation in returns). If you don't model that in, you're going to get results that can;t be achieved in reality. – D Stanley Jul 13 '20 at 15:41
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    @bob another variable you need to take into account is the mortgage interest tax deduction, so it matters what your income (if any) is over the 30 years and if you will be taking the standard deduction – Hatman Jul 13 '20 at 17:15
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    Another less calculable variable is risk... under the 15 year mortgage, you will have higher monthly payments which could be harder to pay if you lose your job or suddenly have reduced income. But on the other hand, under the 30 year plan, you have to wait twice as long until you are risk-free from such considerations; you could lose your job and your house after 20 years. – GendoIkari Jul 15 '20 at 19:15
  • FYI - I've met Harry Sit, the blogger at The Financial Buff. Nice guy. His math is fine. But his assumption, a 5% return, assumes a forecast in the lower 12% (i.e. of the 100 rolling returns in my spreadsheet, 12 are below 5%. He also assumes a 15% cap gain rate, while for many, the cap gain can be 10% or zero. I respect him, but disagree with his conclusion. – JTP - Apologise to Monica Jul 18 '20 at 0:17
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A quick sketch

n = 12
s = 240000

Periodic rate and periodic payment for 15 year and 30 year mortgages

p15 = 2.852/100/n
pp15 = (s p15)/(1 - (1 + p15)^(-n 15)) = 1640.37

p30 = 3.568/100/n
pp30 = (s p30)/(1 - (1 + p30)^(-n 30)) = 1086.84

The 30 year scenario can save $553.53 into the fund at the end of each month.

sv30 = pp15 - pp30 = 553.528

The 30 year scenario pays 30 years of $553.53 (sv30) into the fund.

totalsv30 = (sv30 ((1 + 4/100/n)^(n 30) - 1))/(4/100/n) = 384176

The 15 year scenario pays 15 years of $1640.37 (pp15) into the fund.

totalsv15 = (pp15 ((1 + 4/100/n)^(n 15) - 1))/(4/100/n) = 403679

The 15 year scenario's fund value comes out $19.5k better.

totalsv15 - totalsv30 = 19503

Both scenarios have paid their $240k mortgage and both paid out $590,532.

30 n pp15 = 590532
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  • 0.04/100/n should these calculations be something like 0.04/n or 4/100/n? – rhavelka Jul 15 '20 at 21:14
  • @rhavelka Thanks for noticing that. I have corrected my answer. – Chris Degnen Jul 15 '20 at 21:36
  • This is great, thank you! Do totalsv15 and totalsv30 need the one time 15% capital gains tax applied? – Bob Jul 16 '20 at 13:40
  • @Bob I left the 15% deduction out for clarity. – Chris Degnen Jul 16 '20 at 13:44
  • Showing the math like this without discussion of the variability is misleading, and I think doesn't form a complete answer. – Grade 'Eh' Bacon Jul 17 '20 at 13:02
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I think that looking at long term historical data has value here. I created a spreadsheet which took the S&P returns for Years from 1900-2018, and calculated the 15 yr returns starting with 1919 to have the last 100 rolling 15-yr returns. Then I sorted to see how these numbers were distributed.

The top 50 results were over 9.88%, with the highest being 19.10%

The next 25 results ranged 6.55% to 9.78%

The next 15 results ranged 4.63% to 6.54%

The next 5 results ranged 4.13% to 4.44%

The bottom 5, the worst results were .73%, 1.93%, 2.62%, 2.74%, 3.51%

My conclusion? Those who take the 30 and invest the difference are very likely (95%+) to achieve a successful outcome, accumulating a greater balance than the mortgage still owed, after the 15 years have passed.

I'll pause here and say that I acknowledge that "past performance is no guarantee of future results", and "your results may vary." But this is the best we have. My conclusion would be very different if the S&P returns averaged 4-5%, of course.

And, there are those who would say that a 15 year return isn't quite the same as DCA (dollar cost averaging) by making the purchases each month/year over that same period. To this, I agree. I suspect, however that the results for that quite larger effort would only differ very slightly at the margin, and given the nature of DCA, i.e. 'buy more at lower prices, less at higher' they would actually improve.

For those pursuing such a decision, I'd suggest getting comfortable with a spreadsheet and analyzing the data to your own satisfaction. If OP is wondering why I used 15 when the comparison is 15 vs 30, simple. It's 15 years hence. You are looking to see how successful your plan was. You look at 2 statements, the mortgage balance and the brokerage statement. If, at this point, the brokerage account is higher, you are happy. If it's close or slightly lower, not so much. If the latter were true, there's still the next 15 years to make up for it, and history shows that after a bad decade we are more likely to have a better one, so for the very disciplined, staying the course with your decision is best.

From my own experience, I wrote an article, "Retired, with Mortgage" where I offer that after 15 years of following my own advice "the 401(k) had $349K extra vs our $265K mortgage" and noted that this time period, the 15 years ending in 2012, contained 2 market crashes. I'll also quote, "Two years have since passed, and the market in 2013 and 14 was very rewarding. A gain of over 50%. We ended 2014 with the mortgage at $233K and the calculated 401(k) extra funds at $453K."

In our case, the interest is deductible, so our 3.5% mortgage is really costing 2.73%, for whatever that's worth. I understand yours is not deductible, but if the numbers were so close for a decision I'd stay clear. You can see that the 5th worst rolling period was 3.51% vs 2.74% for the 4th worst. Either way, a 96%/95% chance of success.

One last point before I wrap up. The numbers here assume 100% discipline. For 180 months, making the deposits of the difference between payments. If you or partner have any risk that the growing pile of cash is a temptation, then paying off the mortgage at a faster pace is best. Of course, ten years later (you'd send even more money that the amount due, right?), you'll have a paid off house, no mortgage and a large bump in free cash. Then what? Will you suddenly get responsible? At that point, if you were to lose your job, there are still bills to pay, including property tax. Whether I've done everything perfectly (I haven't) or not, I've always slept better knowing I had a buffer of money, whether it be the retirement accounts or a pre-arranged HELOC. That's worth more than the fully paid house but no liquidity in a tough time. We practiced that right until the layoffs came in 2012 and my wife and I were fired. Which led to our decision to retire early.

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  • I think a simple conclusion on your 2nd paragraph could help the OP based on the apparent level of their understanding: only in 3 of 100 15-year rolling year periods, was the return on the market lower than your after-tax mortgage interest. – Grade 'Eh' Bacon Jul 17 '20 at 13:06
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    I talk too much. Ask my wife. – JTP - Apologise to Monica Jul 17 '20 at 13:07
  • I'm confused by your section about DCA. How is DCA relevant to this question? – Kevin Jul 17 '20 at 15:30
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    @Kevin - the investment isn't lump sum. OP is not depositing a single amount and letting it grow for 15 years. He is investing stream of deposits. When I take a rolling 15 years of returns and calculate the CAGR, it fails to have the precision one would have if the extra layer of math was done, setting up the spreadsheet to give the precise result of those deposits. Consider this - If I enjoy a 32% return (as i saw in 2013) early on, the account might have only had a years worth of deposits. But 32% in year 15? Jackpot. – JTP - Apologise to Monica Jul 17 '20 at 18:15
  • DCA is a strategy used when you have a large sum of money. That is not the case here. DCA is not relevant – Kevin Jul 17 '20 at 18:19

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