A friend asks:
My wife and I have recently purchased a home that we can comfortably afford. We have extra money in our budget that we’d like to put to use, but are not sure whether we should pay down our mortgage or invest the money in the stock market. Which is better?
Paying down debt can be a good thing, and far be it from me to dissuade anyone from that. A dispassionate look at the numbers, however, reveals what might be a surprise to some: if you can save and invest with discipline, paying down your mortgage is typically not a better investment than long-term investing in the stock market.
For the purposes of this analysis, we will use a home price of $400,000 and an interest rate of 4% APY. These are made up numbers that I’m using to keep the math clean, but are not far off from Zillow’s estimated median home price in Austin and typical mortgage rates.
Why you think you should pay down your mortgage
| Month N | Payment Amt | Interest Amt | Pct to Interest |
|---|---|---|---|
| 1 | $1893.21 | $1309.50 | 69.2% |
| 2 | $1893.21 | $1307.58 | 69.1% |
| … | |||
| 149 | $1893.21 | $946.37 | 50.0% |
| 150 | $1893.21 | $943.27 | 49.8% |
| … | |||
| 360 | $1893.21 | $6.18 | 0.3% |
The numbers are depressing, and are even worse if you have a higher interest rate on your loan. With such a small percent of the early payments going to paying down principal — less than one third of the full payment — piling additional principal payments can seem attractive. And, the math does suggest around a decent ROI for lump-sum (i.e. applied directly to principal) payments in the early months of a 30-year mortgage.
| A lump sum of… | Saves you an add’l… | And you’re paid off… |
|---|---|---|
| $1,000 | $2,228 | 1 month sooner |
| $2,000 | $4,439 | 3 months sooner |
| $5,000 | $1,0967 | 8 months sooner |
It takes little creativity to notice a pattern in this table: early lump-sum payments made directly to principal on our loan provides a roughly 220% ROI over 10 years. This might seem surprising; in fact, it should not be, because all we are doing is purchasing debt back from the bank at the same interest rate of our loan. For an i-rate investment over a N-year time period, one would expect a return of:
ROI = (1+i) ^ N – 1
ROI = (1 + 0.04) ^ 30 – 1 = 2.2
It might be surprising that a payment of $1000 saves you over 2x as much from your loan payments, but that really speaks more to how difficult it is to develop an intuition for compounded interest than anything else.
What about the S&P?
ROI = (1+i) ^ N – 1
ROI = (1 + 0.08) ^ 30 – 1 = 9.06
You don’t need any specialized math training to know that in the (1+i)^N term, a bigger value of i is going to give you a bigger result. However, it might surprise you how much bigger a doubling of interest rate from 4% to 8% makes your 30-year return. While a lump-sum payment of $5000 at the beginning of your mortgage saved you almost $11k, a lump-sum investment of $5000 at the same time would have netted you a whopping $45k over your initial $5000 investment, over the same 30-year time period.
This might sound incredible. And, really, it is — the power of compound interest is an awesome one, and it’s amazing that more people don’t make use of it. The snowballing effect of paying down your mortgage is remarkable, but it’s a pittance compared to the return you can get if you allocate your money more productively.
We might think of this another way. If you decide to pay down your mortgage instead of investing in stocks, how much does that decision cost you?
| A lump sum of… | To principal… | To S&P… | Difference |
|---|---|---|---|
| $1,000 | $2,228 | $9,062 | $6,834 |
| $2,000 | $4,439 | $18,125 | $13,686 |
| $5,000 | $10,967 | $45,313 | $34,346 |
The difference between paying down your mortgage versus investing in the S&P is visually dramatic, as well. I’ve adjusted the numbers a bit for graphical acuity; below we have a $400,000 loan at 4% compared with a 7% ROI for the S&P. The lump-sum payment is larger here — $50,000 — and is made in year 3 to make the stair-step more prominent. The mortgage paydown case has us paying off our mortgage five years early, but after 35 years, our net worth is clearly much lower than if we had put the $50,000 in the S&P. In fact, even if paying down your mortgage quickly is a concern, you would be better off putting your lump sum in the S&P and using the proceeds to pay off your mortgage around year 22 when your investment portfolio surpasses the remaining value of your mortgage.
