Extra Mortgage Principal Payment Math

Was just reading an article here and seems confusing: Making extra mortgage payments? Not so fast

I was trying to figure out the reasoning behind some of their bullet points in 1 and 2. Maybe I’m just missing something and someone can explain to me.

For example, assume you have a 30-year mortgage with a monthly payment of \$2,000. Your first payment includes about \$360 in principal and \$1,640 in interest, while the last payment includes about \$60 in interest and \$1,940 in principal. If you made a double payment of \$4,000 (to “save” on interest), all you’re saving is \$60, and that’s 30 years from now. Put another way, it’s a return of less than 0.1% per year.

Wouldn’t your overall interest decrease per month from the slightly lower principal amount as well so it’s not really just \$60?

For example, suppose you have a 30-year loan of \$419,000 at 4% interest. Your standard monthly payment of principal plus interest would be \$2,005. If you paid an extra \$2,000 per month, you’d save almost \$204,000 in interest and pay the loan off in under 11 years, shaving about 19 years off your payment schedule. Sounds pretty good, right? Not so fast. It might not be the best use of your money. Here’s why:
Suppose instead of making extra payments, you deposited the \$2,000 per month in an account earning that same 4% per year. You would have contributed a total \$720,000 plus earned \$679,000 on that sum, for a grand total of nearly \$1.4 million. Since you didn’t pay off the mortgage early, you would still pay around \$300,000 in interest over the course of 30 years, but you would end up \$379,000 ahead. That handily beats the \$204,000 you would have saved by prepaying the mortgage.

If you ignore the tax implications and assume that you could have a 4% savings account, why is there a difference?

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For #1 they’re arguing that if you have 360 payments:
1…2…3…360

and you pay 2x one month you lob \$2000 from your principle. When you get to the end of your payments you’ll have one less payment. Which means you’ll now you have 359 payments:
1…2…3…359. You eliminated the 360th payment, and the \$60 inflation adjusted interest you would have paid in 29.9 years.

For #2:
You pay the extra \$2k a month and walk away at the end of 11 years with a house and no debt. If you put that into a 4% account you could compound the interest.

Basically, you would have 30 years of compounding interest vs. 11 years of simple interest and 19 years of compounding interest.

That’s my best guess.

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It’s a dumb article.

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Yes that first example clearly has a “mistake” where they assume the interest is set in stone per payment and not based on the current loan balance. The “return” on extra payments is the loan’s APR. If the payment would have gone into long term investment instead, then it’s APR minus opportunity cost.

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The author allegedly has a PhD.

I wonder what its in?

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A PhD in making up examples just to prove a point.

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The article is very misleading. Each payment you make at the beginning of the loan reduces your principal and thereby reduces you succeeding interest. Is the bank trying to discourage prepayment??

Good point. I didn’t find the type of PhD but I didn’t look too hard. He also has some other acronyms. I wonder how they stack up to a CFP, etc.

http://www.ain-services.com/Our-Team

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Okay, I think there’s no difference mathematically regarding #1 and #2. I’m not sure how to prove #1, but at least for #2, I forgot to invest that extra \$2k for an additional 19 years which comes out to \$679k.

Perhaps now the question is what’s more beneficial tax-wise given example #2.

You get the mortgage interest deduction for 30 years vs 11, but you also pay tax on that extra 11 years of interest at your income level. It seems that the mortgage deduction and extra interest tax would balance out. However, if you invested in an index fund, then you could get the mortgage deduction but then pay long term capital gains at a lower rate.

Not really. How payments are applied may be a matter of contract or the mortgage servicer’s practices. Many times, if the payment is not directed, it will be applied to a future payment and not principal.

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That’s a good point about if you’re just making a future payment or principal payment. You’re definitely getting screwed if you’re just making a future payment.

I doubt this is true. You could run the numbers…

Also, keep in mind that capital gains may not apply depending on the investment vehicle.

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Extra payments are very easy to specify… especially with so many firms now having online payments.

You did not forget. The author is comparing (1) the amount saved on interest from investing \$2000/mo for 11 years with (2) an amount earned in interest by investing \$2000/mo for 30 years. That comparison is ridiculous, since the two investments are not equivalent.

Investing at 4% is exactly equivalent to paying off a 4% mortgage, as you guessed in your OP. It’s a 4% ROI either way.

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Keep in mind that while interest income is taxed at your marginal tax rate, the ability to take advantage of the mortgage interest deduction depends on the individual tax situation and the savings may not be at the marginal tax rate.

Gaining anything from the mortgage interest deduction requires your itemized deductions to exceed the standard deduction, which isn’t the case for most tax payers and was made even less likely last year with the increased standard deduction and the \$10K SALT limit.

In order to gain the full tax benefit (at your marginal rate) from a single deduction (say the mortgage interest), the rest of your itemized deductions must be >= the standard deduction. Otherwise you’re not reducing your tax bill at your marginal rate.

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If you’re paying extra this way you can also ask your mortgage servicer to “recast” your mortgage at a later date in order to reduce your monthly payments on the original 30 yr timeframe, in case the investment/paying off house calculus changes. It usually costs a few hundred bucks.

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