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My wife and I have multiple loans to pay off: car loans, student loans, and a mortgage.

Currently we pay the minimum on all but one of the loans, and put any extra we'd like to pay into the highest-interest loan. We do this because, mathematically, it will lead to the lowest overall interest.

However, as a mathematician, I only know numbers. The real world is much more colorful and scary.

So is there some reason to pay more than the minimum on our other loans? For example: better for our credit score; legal reasons; some other benefit..?

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    The only reason I can think of is to get your mortgage below the threshold where you don't have to pay for PMI. Of course you'd have to crunch some numbers to see if this applies to you.
    – jamesqf
    Apr 22, 2015 at 5:05
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    I'm not a financial advisor I'm really just a beginner. Private Student loans are for life. You can't bankrupt yourself as a way to get out of them. They to me seem the most dangerous. However I know nothing about thresholds and all that. But I would pay off the highest % loan, and if that wasn't the student loan, I'ld split it among the highest and the student loan. But as I said, complete newbie here
    – Mallow
    Apr 22, 2015 at 12:33
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    When paying minimum on all but one, since you are throwing extra at one loan it seems that if for example your student loan and car loan were similar balances but one (car) was a much higher monthly payment, then pay that one off first so that you now have more extra to throw at the next one.
    – AbraCadaver
    Apr 22, 2015 at 20:40
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    @AbraCadaver: No, mathematically you are incorrect. If I owe $10k total and I am paying $1k off a month, then my overall debt goes down by $1k, regardless if I am splitting that amongst multiple loans or putting it all into a single one. The only thing that matters is minimizing the interest that is generated, which can be done by putting as much of that $1k as possible into the highest-interest loan. If that loan is different from the "highest payment" loan, then your strategy is non-optimal.
    – BlueRaja - Danny Pflughoeft
    Apr 22, 2015 at 21:32
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    @AbraCadaver - is that allowed? As I understood it, the word of the David is infallible, it's to be followed to the letter of the law, lest you appear to be a heretic.
    – JTP - Apologise to Monica ♦
    Apr 23, 2015 at 23:37

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mhoran mentioned PMI. One can look at a PMI encumbered loan this way: the rate on the loan is the mortgage rate for the lower 78% of loan to value. The rest of the loan has a true rate that has to include the PMI cost. Mathematically, it's as if you had two loans, a fixed rate, and a high priced second mortgage. If the $20k you need to pay down to eliminate PMI has a monthly $100 cost, the rate on that money should be viewed as 6% above the mortgage rate you already pay.

A credit card with too high a utization can ding your credit score short term. Regardless of total utilization.

Aside from these two issues, adjust the rates for taxes, eg my 3.5% mortgage is really 2.6%, and stick with the plan to sort by rate to pay off.

Too many expensive mistakes are made based on emotion. If you have the discipline of a mathematician go with the numbers. Keep in mind, millions 'feel' good about a tax refund. When anyone tells you they got a big refund, they are bragging they planned poorly, lent the government money interest free, and are too ignorant to understand either point. I always respond "that's great" and fake a smile.

The debt snowball method is a cult that may provide an emotional win. No mathematician should belong to that cult.

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  • "adjust the rates for taxes, eg my 3.5% mortgage is really 2.6%" - I don't understand this comment. What do taxes have to do with anything? (I don't know how mortgage-related taxes work at all)
    – BlueRaja - Danny Pflughoeft
    Apr 22, 2015 at 23:10
  • When interest on a debt is deductible on one's taxes, one should adjust the rate to get an adjusted post tax figure.
    – JTP - Apologise to Monica ♦
    Apr 23, 2015 at 23:32
  • How does this address the question of whether or not it makes sense to pay extra on more than one debt at a time? You still have the OP choosing which debt is the worst, and paying that one off first.
    – Ben Miller
    Apr 24, 2015 at 15:38
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The reason to pay off a loan with a lower rate first is if there are thresholds involved. Also keep in mind you have to factor in if any of the loans are tax deductible.

What are some thresholds:

  • an amount that will allow you to drop PMI on the mortgage.
  • getting a loan to zero. This allows you to eliminate one debt which is a psychological boost. Paying off the debt allows you to snowball its minimum payment in to the other debts the following months.

You may ask why eliminate the single debt when it doesn't gain you anything mathematically. This goes in the some other benefit category.

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Not any practical reasons that will make the higher interest cost worth it. If these loans all have a fixed rate, it makes sense to make larger payments towards the one with the highest interest rate.

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Be aware that if any of your credit cards has balances that are being charged different rates, then paying the minimum payment due shown on a monthly statement will almost certainly get applied to that part of the balance that is being charged the lowest rate (including a 0% rate if you accepted a 0% balance transfer offer or used one of those "convenience checks" that the card companies send their customers to use in creating a 0% rate balance). It is only any amounts that exceed the minimum payment due on a card that must, (by law), be applied to the highest-interest balance for that card. So, if the balance on a card has parts being charged different rates, it can be misleading to use an average interest rate for that card in making comparisons regarding which card has the highest interest rate.

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  • Even if I had mentioned credit cards (which I didn't), I don't understand how this is an answer to the question.
    – BlueRaja - Danny Pflughoeft
    Apr 22, 2015 at 23:13
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    @BlueRaja-DannyPflughoeft It means you should double check the interest rates on your debts to ensure you are directing your payments to the highest actual interest rate.
    – Eric
    Apr 23, 2015 at 12:51
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    @BlueRaja-DannyPflughoeft In addition to what Eric said, it is important to check how exactly any additional payment is applied to your car loan, say. I have had auto loans in which, if the monthly payment was $300 and I paid $400 one month, the extra amount merely reduced the payment due the next month to $200, and did not at all reduce the principal amount owed. In effect, they held the money (without paying me any interest) and applied it towards the next monthly payment. That extra payment did not help at all. So, please read your loan agreements. The devil is indeed in the details.
    – Dilip Sarwate
    Apr 23, 2015 at 20:23
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Check the conditions of each loan. There are plenty of credit cards where the interest rate changes, depending on whether you pay just the minimum, a higher amount, or a much higher amount. As a mathematician, you will enjoy that this makes the problem of optimal payment amounts much more interesting.

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    Could you tell us the names of some cards that lower your interest rate if the payment is more than just the minimum?
    – Dilip Sarwate
    Apr 22, 2015 at 1:55
  • Barclays Bank in the UK. About every credit card in the UK. And I wouldn't say they decrease the rate if you pay more than the minimum, I'd say they increase the rate if you pay just the minimum.
    – gnasher729
    May 18, 2015 at 20:28

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