I construct a spreadsheet to investigate when is the best time to pay off a house loan.
In my model, there are two factors at work:
- The real estate appreciation rate, in this case I set it to 5%
- The Interest rate charged on the mortgage loan, I set it to 4%
and I assume that the rental income collected is exactly the same as the annuity monthly payment and used to offset it, to avoid complications in terms of compounding interest charge on the mortgage loan.
Assuming 30 years mortgage, when is the best time to pay of the house loan given the above information?
The formula for compound gain, r:
(1+r)^n = Total amount after selling/Total amount invested
Given that the house is appreciating faster than the interest rate ( 5% vs. 4%), and given that in the beginning of the mortgage, most of the payment goes to the interest ( very little equity accrued), I would expect that the longer into the mortgage years, the higher the compound gain ( in % terms). So the maximum compound gain should occur at the end of mortgage loan, in this case it is 30 years.
But this is not what I found; instead, I found that the maximum compound gain occurs at somewhere between around year 5.
Playing around with the interest rate, downpayment, appreciation rate and other variables confirms one thing, that maximum compound gain will not always occur when the mortgage matures at 30 years. Instead, it's occurring somewhere in the middle, from year 5 to year 20 quite frequently.
It seems that there is a time to settle the full house loan, and it's not at the end of mortgage term, despite that the house appreciates faster than interest rates on the loan.
I've no idea why this is so, any explanation?
- Some object that the appreciation rate is higher than inflation/mortgage loan rate, but this is besides the point. If anything, higher appreciation rate should mean that the the maximum compound gain should happen at the end of mortgage. But it's not, and this is why I'm asking the question.
- Even if you set the appreciation rate to be the same as mortgage loan rate, the same conclusion still applies in some situation, eg:
selling charge=0%, and
annual interest=annual appreciation=4%.
- I'm aware that I'm ignoring the tax, and do a few simplifications. But I am not looking forward to invest in real estate just based on this spreadsheet. I do the spreadsheet ( a toy example) for the purpose of pointing out a puzzling observation
- Even when the rent is inflation-adjusted, and the management fees and gain tax is included, the same behavior persists.
- A bug regarding the house price wasn't properly fixed for columns other than the first one in the spreadsheet is fixed. The original conclusion ( namely, the question still stands)
- Another bug regarding the mortgage payment is deducted from final gain is fixed ( it shouldn't, as it's the tenant who pays for the mortgage payment in this contrived example). After fixing, the my results and the answer here results are now the same. But still, the behavior persists.