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tl;dr:
I have two amortized mortgages; one big and one small.
The conditions (interest rate and mortgage length) are exactly the same.
Which should I pay off first?

I have always heard that you should pay off the debt with the highest interest rate first, but in my case I have two mortgages with the exact same conditions (same interest rate and same length). Because of this, I have considered them just one debt, and therefore started to pay extra on the smallest loan. I thought it made no difference financially, but getting rid of one mortgage was a motivation. My logic was that every dollar I pay in early is a dollar I won't pay compound interest on later, and as every dollar has the same interest rate and pay-off length, there shouldn't be a difference which loan I put my dollar on.

However, I just started thinking, and because of the nature of amortized loans, I'm obviously paying quite a lot of interest in the beginning, which means that during the years I spend paying off the small loan, I'm paying a lot of interest and nearly nothing towards the principal on the big one. The loans are for 30 years, and I got them one year ago, so there's 29 years left.

The numbers in question:

  • $59,000, 5.4% annual interest rate, 29 years left
  • $270,000, 5.4% annual interest rate, 29 years left
  • I can pay off $500 extra per month

My calculations are (did some rounding and estimating, so not 100% exact):

Paying off the smallest loan first:

  • Smallest loan done after 7 years. Saved about $47,500.
  • At this point, there's $236,250 left of the big one. Start to pay extra on the big one.
  • Biggest loan done after 14 more years. Saved about $69,580 on this.
  • In total: Done after 21 years, saved $117,080.

Paying off the biggest loan first:

  • Biggest loan done after 17 years. Saved about $124,200.
  • At this point, there's $35,880 left of the small one. Start to pay extra on the small one.
  • Smallest loan done after 4 more years. Saved about $10,680 on this.
  • In total: Done after 21 years, saved $134,880.

Considering them as one loan of $329k:

  • Loan done after 18 years. Saved $135,890.

According to this, paying off the biggest one seems to be fairly close to just considering them as one loan. Close enough that the difference might just be down to my rounding errors. But the 3 year difference, while the total cost remains almost the same, puzzles me a bit.
And paying off the smallest one first seems to cost me about $18,000 compared to paying off the biggest one first. It might not seem like much over such a long time frame, but it averages to about $75 each and every month for the next 20 years, so that is actually a substantial amount in my eyes.

Have I messed up anywhere?
Is it really beneficial to pay off extra on the big mortgage? Or is it no difference, and I should stick to the small one for motivation?

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genbatro
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3 Answers3

42

You haven't accounted for what happens when the small loan is completely paid off.

Seven years into the aggressive payoff schedule you need to shift all original principal and interest payment and the extra $500 to the larger loan. When you do that the different scenarios will almost equal each other. When I checked with a spreadsheet the delta was less than $200, but that was due to the extra payment resulted in a non-zero balances when trying to account for the last payment on a loan.

Because the length and the interest rate are the same for both loans the order doesn't matter from a money standpoint, though one disappears after 7 years so there is some psychological and paperwork benefit.

mhoran_psprep
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11

However, I just started thinking, and because of the nature of amortized loans, I'm obviously paying quite a lot of interest in the beginning....

This is a common point of confusion, the portion of your payment that is interest is only larger at the beginning because your balance is higher. If you look at an amortization schedule you'll see that the monthly interest is the outstanding balance multiplied by the monthly rate (APR/12).

You were correct that you can think of them as one big loan. There seems to be a flaw in your math, likely you are not using the same total payment amount each month for the duration of each scenario.

Hart CO
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You already have two answers, I'll be the guy who go orthogonal: I suggest you consider to not repay any mortgages early.
If you do, there is an associated opportunity cost, of not investing the money used to repay the loans.
Instead, consider putting your cash into stocks or ETF that can return more interest than the loans. JL.Collins, would suggest you to aim for SP500 which got 7% average interests in the past 150 years, therefore more than your 5.4% from the mortgages.
According to Mister Money Mustache forum, you got 75 pages of a topic of discussion on the matter. And an associated later blogpost that suggests your mileage may vary.
There is a question of risk tolerance if your loans are fixed rate and you don't like capital exposure. That would depends on your personality. One tropism that you'll find is "Money now is worth more than money in the future", the banks nicely extended you loads of it, keep it. (which means your leverage is a gift, don't be allergic to it)

v.oddou
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