The hidden math of extra mortgage payments

Don’t pay by anticipation to shorten the loan, and invest the money!

It’s good to lock a 30Y fixed because interest rates are going to go up and up, and the bank allows you to repay more principal than the mortgage premiums to end the mortgage early. But is it to your benefit?

One thing I was told AFTER is that paying by anticipation DOES NOT change your payment schedule… So what does that mean? It means that if you’re paying by anticipation, you’re loaning money to the bank for free. You would be better off holding onto that money (possibly invest it), and using it only at the end to close your mortgage a few years early.

If I’m right then mortgage calculators like this nice one don’t tell you the truth about early payments.

It turns out that when you ask around, your realtor or other folks supposedly here to help you purchase a house won’t really help you, they may not even know where the trickery is, it’s hidden in the pudding, but it’s simple if I figured it out correctly.

Here’s some generic loan numbers, for a $500K loan at 3.5%:

$500K, 30Y fixed 3.5% = 2,245.22/month, for 360 months,
$308,280.34 interest paid total (61.65% total)

Now what about shortening the loan by a decade?

$500K, 20Y fixed 3.5% = $2,899.80/month, for 240 months,
$195,951.66 interest paid total ( 39.19% total)

So with a 20Y fixed, you save $112K. Fact is you would likely have had a lower 3.25% or 3% loan ($180,634.91 or $165,517.12 interest, so that was another 30K in savings).

What about paying by anticipation same monthly sum as a 20Y monthly payment?Well silly me I thought you could just pay in anticipation and get the same math, just at the cost of a slightly higher interest rate of a longer loan… So let’s do the math: What if you pay every month $2,899.80 on the 30Y loan? That’s $654.58 per month extra…

Instead of ending in 2047 the loan end in Nov 2039, two years after the 20 year mortgage, paying $284,226.20 in interest (that’s because the schedule is fixed!), $88.6K more to the bank.

Ok so if you over pay 2 more years, you should compare to a 22 year loan then! Well that loan would have cost $217,657.34. Still 67K less.

To make it clear:

I think a loan schedule calculates the 3.5% interest you owe every year and splits the interest by 12… 500K * (3.5% / 12) = $1458 for the first month interest. Now we want the loan to last 30 years so you have to pay a given principal amount.

This generates  a schedule like so. Now the schedule is fixed. This means that if you pay early, the interest you owe at that time is not recalculated (it should since you now owe less premium), it stays the same just following the schedule, you only reduced the principal, without changing the interest you pay monthly.

If you kept the money in the bank and just plunked these $176,736.60 to close the mortgage on Nov 2039, you would not have given the lender a penny more…

In fact if you kept that money invested at 3.5% you would break with a 20Y mortgage, gaining $91,538.79 of interest for a total of $268,275.39 in oc 2039. My math must be wrong because it shows you could end the loan in April 2027, not Dec 2037…


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