“There have been no 20 year periods where the market has returned less than 4%”

That doesn’t sound right to me. Look at the 20 year periods starting between 1/1929-12/1929 and you’ll find they are all under 4% and one as low as 2.05%. You might be looking at data that doesn’t go that far back…what source are you using?

No matter what the returns are for a 20 year period, when you are analyzing a series of cash flows, you cannot assume that the return for each cash flow within the 20 year period will receive the long term (20-year) average return. Only the very first cash flow (that is held for 20 years) will.

To illustrate my point, look at the last 19 years, where the compounded return (with dividend reinvestment) was 7.25%, i.e., the first monthly ($100) investment received this return. Each subsequent monthly ($100) investment, however, received a different compounded return–some greater than and many less than 7.25% (quite a few were negative). Overall, a series of $100 monthly payments over the last 19 years would have grown to $35,200 or provide an average compounded return of 4.31%. As you see, 7.25% 19-year lump sum return is much different than the actual return you received from the series of period cash flows over the same period.

Don’t get me wrong, I liked your example because it shows (in a very understandable way) that if you have extra money to invest and can reliably get a higher rate of return than your mortgage interest, you would be better off investing than paying down your mortgage. What I thought deserved a little more discussion, however, was the reliability of market returns for a series of cash flows, i.e., that a series of cash flows over a long period often has a rate of return that is quite a bit more speculative than the lump sum return over the same period the example uses.

No reason to pay down your mortgage for a hugely non-trivial number of people, huh?

From what I’ve read, if you hold long enough the market historically will provide you a 9.5% return (not including taxes/expenses/etc). Regardless of whether the average market return is 9.5% or 11.5%, the length of your holding period determines the swing around the average market return that you can expect to receive. Thus, Person B, by holding longer, is just increasing their chances of receiving the average market return–increases the reliability of the return.

“On balance, I think that person B is actually holding MORE money for LONGER periods in the stock market …”

Person B is definitely in the market for LONGER period than Persion A…but doesn’t ‘necessarily’ have more money in the market. If Person B does not receive a higher return from the market than the mortgage interest (5%) over the first 19 years, there is a good chance that Person A will have more money in the market by the time Person B pays off their mortgage (and also at the end of the 44 year period).

In most cases Person B will be better off at the end of the 44 years, but there are a non-trival number of cases where Person A will be better off.

One word of caution, however…when analyzing a series of cash flows for a specific evaluation period, such as the monthly investments described in the post, each of those cash flows has a different holding period. For instance, the first $100 investment made by person B has a holding period of 44 years…but each subsequent investment will be held for less time. As the holding periods get smaller and smaller, the accuracy of the estimated 8% return lessens. In other words, the assumption that an index fund will provide an 8% return for monthly investments that will be held for less than 25-30 years is a little more speculative than the post makes it seem.

That being said, it probably does not make a difference in this example because the shortest holding period where person A and person B made different investments is 19 years.

So, unless the total basis of macro economics in the US – and globally – has permanently changed … HELL YES

@ Scott – I bet it was the best hour or so that you ever spent with a spreadsheet and/or online calculator!

The difference between the two scenarios over a 30 yr period where staggering. It was a difference of over 1.5 million dollars added to my portfolio by not paying off my mortgage early.