Repair-It

I resisted the urge to insert a "Fun with" prefix to this thread's title, even though it's true (for me). I was struggling with the math of overpaying my mortgage. Let me show the two scenarios which are tailored to be my actual situation.

Case 1: My current mortgage (remember I got my rate down to 4.125% from 5.875% for a modest $1,000 fee, so the "borrowed" amount changed to what it was when that rate change occurred, for calculation purposes) I focused on the total interest paid (at least from my rate change point to the end of the loan), which you can see is $114,071.73.

Now Case 2, which is my current mortgage but paying an extra $273.10 per month. Oh nice, total interest is down to $74,758.47. That saved $39,313.26. Except now look at the box titled "total early payments." I threw an extra $55,985.50 at the loan and saved less than $40k! Paying off early is bogus, right? Wrong. I omitted a key piece of information.

I omitted total actual mortgage payments. See, by paying that extra $273.10 each month, I actually shaved nearly 8 years off the loan. Where am I going with this?

Look at Case 1 again. Total payments = $1,009.47 * 300 months = $302,841.00.

Now look at Case 2 again. Total payments = $1,282.57 * 206 months = $264,209.42.

Eureka. I actually save another $38,631.58 in mortgage payments, in addition to the $39,313.26 that I save in interest, saving me a grand total of $77,944.84. Now, if I can do better than an average 39% marginal rate of return over the next 17 years, which is like 2% per year, then maybe I should take the investment. This also doesn't take into account the time value of money.

But I think I'll take the mortgage overpayment. It is a guaranteed return (anything over my 0.9% online savings is NOT guaranteed), and does also provide a psychological benefit. Considering inflation averages 3% per year, money in FY2014 dollars is only worth 60.5% in 2031 (when I would theoretically pay off my mortgage).

So let's take that overpayment and put it into an account that gives a return of an aggressive 5% per year. That gives me $86,960.48 after 17 years. That's worth exactly $52,612.52 in 2031 (in today's dollars). The downer is I put in $55,712.40 over the life of that investment and it is actually worth less in year 17. But if I put that money in a mattress (or a worthless savings account with practically no interest) my $55,712.40 would only be worth $33,706.00. So investing was still better, obviously. But was it better than paying off my mortgage early with that money instead? Technically, if you compare both uncorrected values, it appears to be a $9,015.64 better investment. A rate of 3.8% annually would equate to the same value as overpaying my mortgage.

BUT, given the certainty of the return from paying off my mortgage early (remember, it is a GUARANTEED return), and the relative UNcertainty of this 5% annual investment return (or even a 3.8% annual return), I'll take overpayment.

Something about this doesn't seem right. I will revisit soon.

Ok. I had the right idea but I overcomplicated it. I also under exaggerated the benefit of overpaying my mortgage.

If I can take $55,985.50 and come out with $39,313.26 of interest savings, then that's a return of 70.2%. But we need to multiply the interest savings by 0.605 because the benefit is decreased due to inflation. So that gives a return of 42.5%, which is close enough to the 39% I used above.

So let me run the numbers again. Let me run them not taking into account the time value of money, because I think it would cancel out in my scenario (both cases involve a monthly payout to enable the "investment").

Paying the mortgage off early means a return of $39,313.26, which is 70.2%, over the 17 years that it takes to pay the loan off early.

If I took that over payment of $273.10 each month and put it into an investment account that had an interest rate of 5% (compounded continuously), that would give me a return of $32,276.47, also uncorrected for inflation. That translates to a total gain of 57.9%. I would need an annual APY of 5.95% to match my early payoff return. Remember, my 70.2% return is guaranteed. It's a fixed rate, and amortization is known. Where can I get 5.95% per year guaranteed? Nowhere.