Someone tell me what’s wrong with this calculation? The “common sense” advice is that one should always take the shorter amortization period that you can live with when buying a mortgage, all other things being equal. When I crunch the numbers, however, it doesn’t make sense.
I whipped up a simple spreadsheet that does the major calculations: http://spreadsheets.google.com/pub?key=p4BfPAlbI_wk4TRtdFKA0MQ
I picked an arbitrary principal amount. I also picked the amortization period in a similar fashion. It’s easy to spot that five years doesn’t make a large difference in the monthly payments. However, if we assume that monthly difference is invested for a certain Return On Investment, it adds up to a pretty big amount after 30 years.
For fun, I factored in the tax refund form using a tax shelter – it makes the case stronger, but it doesn’t change the conclusion. I also took into account that with a shorter amortization period, the last 5 years of payments goes directly into the bank account.
Can someone tell me why these calculations are wrong? It runs contrary to all the accepted wisdom about mortgages. I ignored inflation, but given that inflation is economically beneficial when holding debt, it would make extending the amortization period a better case. The ROI is chosen based on a historical average of the stock market index, and the mortgage rate seems historically reasonable, too?
My only thought so far is that the underlying assumption in the standard advice is that people won’t (profitably) invest the extra monthly cash that comes from a smaller payments. Is it really simply a discipline issue, and knowing one’s self?
[Updated 2007/01/26] The comment from DX is right; if I remove the tax shelter effects and make the mortgage rate equal to the ROI, the Future Value of both amortization cases ends up the same. Another consideration I’m wondering about is if the Present Value of those last five years of mortgage-free savings is as valuable as the accrual of smaller savings earlier. I suspect, however, that is balanced out by the reduced real burden of debt due to that same effect.
So I guess it boils down to whether one’s expected ROI is greater than the mortgage rate, and whether one is forgoing any tax shelters with those mortgage payments.
