Very good Ben, in a more simplistic form: If debt was about math only, we would not have payday lenders, 21% + credit cards, or sub-prime car loans. Yet these things are prevalent.

Debt reduction is often about behavior modification. As such small wins are necessary to keep going much like a 12 step program; or, gamification as Ben pointed out.

The funny thing is that if a person becomes and stays intense on a debt reduction program, interest rate "inefficiency" is dwarfed by extra income or increased austerity.

TL/DR

Yes, The David popularized the Debt Snowball. The method of paying low balance first. It's purely psychological. The reward or sense of accomplishment is a motivator to keep pushing to the next card.

There's also the good feeling of following one you believe to be wise. The David is very charismatic, and speaks in a no-nonsense my way or the highway voice. History is riddled with religious leaders who offer advice which is followed without question.

The good feeling, in theory, leads to a greater success rate. And really, it's easier to follow a plan that comes at a cost than to follow one that your guru takes issue with.

In the end, when I produce a spreadsheet showing the cost difference, say $1000 over a 3 year period, the response is that it's worth the $1000 to actually succeed. My sole purpose is to simply point out the cost difference between the two methods. $100? Go with the one that makes you feel good. $2000? Just think about it first.

If it's not clear, my issue is less with the fact that the low balance method is inferior and more with its proponents wishing to obfuscate the fact that the high interest method is not only valid but has some savings built in. When a woman called into The David's radio show and said her friend recommended the high rate first method, he dismissed it, and told her that low balance was the only way to go.

The rest of this answer is tangent to the real issue, answered above.

The battle reminds me of how people brag about getting a tax refund. With all due respect to the Tax Software people, the goal should be minimizing one's tax bill. Getting a high refund means you misplanned all year, and lent Uncle Sam money at zero interest(1). And yet you feel good about getting $3000 back in April. (Disclosure - when my father in law passed away, I took over my mother in law's finances. Her IRA RMD, and taxes. First year, I converted some money to Roth, and we had a $100 tax bill. Frowny face on mom. Since then, I have Schwab hold too much federal tax, and we always get about $100 back. This makes her happy, and I'll ignore the 27 cents lost interest.)

(1) - I need to acknowledge that there are cases where the taxpayer has had zero dollars withheld, yet receives a 'tax refund.' The earned income tax credit (EITC) produces a refundable benefit, i.e. a payment that's not conditional on tax due. Obviously, those who benefit from this are not whom I am talking about.

Also, in response to a comment below, the opportunity cost is not the sub-1% rate the bank would have paid you on the money had you held on to it. It's the 18% card you should be paying off. That $3000 refund likely cost over $400 in the interest paid over the prior year.

In some cases, it might be rational to pay low-interest debt first, because the consequences of defaulting on that debt are worse.

Consider this simplified example. Suppose you have two debts: a low-interest mortgage, secured by your house, and a high-interest unsecured credit card debt, both of which are within a few years of being paid off. There is a chance that sometime between now and then, something will happen to disrupt your income (e.g. medical problems), and it won't be possible to make the payments on either loan.

Defaulting on the credit card loan will result in a lower credit score and calls from collection agencies. Defaulting on the mortgage will result in the foreclosure or forced sale of your house, at best forcing you to move, and at worst leaving you homeless, at a time when you are also facing other (e.g. medical) problems. So you might rationally judge that losing your house is much worse than bad credit. Therefore, you might rationally conclude that it would be better to direct extra income toward paying down the mortgage, to increase the chances that, if and when an income disruption might occur, the mortgage would already be paid off. In other words, you shorten the window of time where income disruption results in foreclosure.

You might decide that this increased security is worth the extra interest you will pay, compared to the strategy where you pay the high-interest loan first.

This is a fairly special situation, but you asked "Why might it be a good idea to do this?", and I am just giving an example where it could rationally be considered a good idea.

(Of course, in a real-life version of this example, there might be other options available, such as refinancing the mortgage. If you like, you could imagine a more extreme example where the lower-interest debt is owed to Joey Knuckles the loanshark, who will come and break your kneecaps if you miss a payment.)

I wouldn't advocate it, but one reason to pay a lower interest rate is if you have $990 on a $1000 limit credit card with 6% interest and $5000 on a $15k limit card at 10% interest. Having $500 to pay in a month and putting it on the lower interest would free up a greater percentage of credit on that card and could potentially help your credit rating I believe.

I think having $1000 on 10 different credit cards w/ $15k limit reflects better than $10k on one $15k card, regardless of interest rates. Personally I think that's dumb b/c having the extra credit available is an opportunity to get into trouble a lot easier.

If the balance on the low rate loan is very high (say, an IBR student loan at 6% that accumulates interest every year), and the balance on the high rate loan (say, a CC at 18%) is comparatively very small, then you'd want to make sure that you've at least "stopped the bleeding" on the high balance loan before starting to pay off the CC.

If you have a debt that has very low interest now, but you are aware that it's not going to stay that way (0% introductory APR on a credit card, for example), it can make sense to pay that off before the higher rate kicks in.

One reason to not do that is if you consider that one of the loans is at risk of being called in early.

e.g. You have a line of credit which is close to its limit, and the bank decides to reduce that limit, forcing you to quickly come up with the money to pay it down below the new limit, which can really throw a wrench into your plans.

It may be the case that some of your debts have a flat regular fee in addition to the interest, which will go away when the debt is completely paid. For example, my mortgage has an approximately $400/year "package fee" as well as its (quite low) interest. When I finish paying the mortgage, I won't have to pay that fee anymore, so it is theoretically possible that spending extra money on paying off my mortgage would be better than spending it on paying off some other debt.

I think it's unlikely that it would actually ever be my optimal move in practice, but the point is, there may be an advantage, financial or otherwise, to getting rid of a particular debt, other than merely removing the burden of interest. Those are special situations, though, and in the majority of cases, starting with the highest interest loan will be the right move.

There are a number of bona fide reasons to consider here.

1. Interest that is tax deductable, or for which a credit can be obtained is not as costly as the nominal APR might suggest.

2. If there is a cost to discharging a security packet, or a mortgage, it may not be convenient if we are advanced in the repayment schedule.

   • Property that is mortgaged, for some small remaining amount, may have documents lodged with the bank as security. This makes it hard for someone else to (fraudulently) borrow against the property, and there may be fees for this custody otherwise.
   • There may be rebates on other products offered by the lender that apply only while this account is active.

   • Early exit fees may apply, or the interest may be "pre-determined".

     3. If you are engineering a default to offload the security or trigger some action that is favourable in the long term.

As a rule of thumb, when we are talking about rates above 10% p.a. then arrangements should be short (bridging finance - keep it short and charge 'em heaps), and for personal arrangements, small.

There are non-financial costs to having a debt: you need to remember to make monthly payments, perhaps keep track of changing interest rates, be aware of conditions of the debt, archive the related paperwork. Life is simpler with fewer debts, and that has value.

Of course, if the difference in interest rate is large, then that is more important and the higher interest should be paid off first. But if the difference is only half a percentage point or so, you may decide that having fewer debts is in itself worth the bit of extra interest you pay.

I recently paid off a line of credit on an investment property that I own. I had some surplus cash and decided to pay off the line of credit rather than to make a principal payment on the primary mortgage with a higher interest rate.

The interest rate on the line of credit was tiny and the balance was also pretty low. My reasoning was that by paying off the line of credit I would be done with that account and would have one less bill to pay each month, one less risk of something going wrong and a late payment hurting my credit, one less statement to reconcile each month, and one less bookkeeping core to manage.

I could have grown my net worth by few couple of dollars each month had I kept the line of credit and made a principal payment on the primary loan. I judged that it wasn't worth the hassle and risks.

This is a slightly different reason to any other answer I have seen here about irrationality and how being rationally aware of one's irrationality (in the future or in different circumstances) can lead you to make decisions which on the face of it seem wrong.

First of all, why do people sometimes maintain balances on high-interest debt when they have savings? Standard advice on many money-management sites and forums is to withdraw the savings to pay down the debt. However, I think there is a problem with this. Suppose you have $5,000 in a savings account, and a $2,000 credit card balance. You are paying more interest on the credit card than you get from the savings account, and it seems that you should withdraw some money from the savings account, and pay off the cc.

However, the difference between the two scenarios, other than the interest you lose by keeping the cc balance, is your motivation for saving. If you have a credit card balance of $2,000, you might be obliged to pay a minimum payment of $100 each month. If you have any extra money, you will be rewarded if you pay more in to the credit card, by seeing the balance go down and understanding that you will soon be free from receiving this awful bill each month. To maintain your savings goal, it's enough to agree with yourself that you won't do any new spending on the cc, or withdraw any savings.

Now suppose that you decide to pay off the cc with the savings. There is now nothing 'forcing' you to save $100 each month. When you get to the end of the month, you have to motivate yourself that you will be adding spare cash to your $3,000 savings balance, rather than that you 'have to' pay down your cc. Yes, if you spend the spare cash instead of saving it, you get something in return for it. But it is possible that spending $140 on small-scale discretionary spending (things you don't need) actually gets you less for your money than paying the credit card company $40 interest and saving $100? You might even be tempted to start spending on your credit card again, knowing that you have a 0 balance, and that you 'can always pay it off out of savings'.

It's easy to analogize this to a situation with two types of debt. Suppose that you have a $2,000 debt to your parents with no interest and a $2,000 loan at high interest, and you get a $2,000 windfall. Let's assume that your parents don't need the money in a hurry and aren't hassling you to pay them (otherwise you could consider the guilt or the hassle as a form of emotional interest rate). Might it not be better to pay your parents off? If you do, you are likely to keep paying off your loan out of necessity of making the regular payments. In 20 paychecks (or whatever) you might be debt free. If you pay off your loan, you lose the incentive to save. After 20 months you still owe your parents $2,000.

I am not saying that this is always what makes sense. Just that it could make sense.

EDIT

Note that this is an opposite to the 'Debt Snowball' method. That method says that it's better to pay off small debts, because that way you have more free cash flow to pay off the larger debts. The above argues that this is a bad idea, because you might spend the increased cash flow on junk. It would be better to keep around as many things as possible which have minimum payments, because it restricts you to paying things rather than gives you the choice of whether to save or spend.

Another unmentioned reason: flexibility and liquidity. There is a fundamental difference between installment and revolving debt, such that it could be rational to pay revolving debt before an amortizing loan.

Lets say you have 100K in cash, a 100K mortgage at 4% and 4 25K credit cards at maximum balance and a 0% promotional rate (at least for now).

If you pay off the mortgage, you may not get liquidity if you need it. This path is not necessarily reversible.

If you pay off the credit cards, you have 100K of credit available to you. You can reverse to the case of having 100K in cash, and 200K in debt.

Let's say I have two loans (say 2 car loans), and the high interest loan has a higher balance. Both have a monthly payment of, say, $500.

My income fluctuates a lot, so occasionally I only have $750. I get hit with big fees those months, or maybe I just have to eat beans.

Lo and behold, I come on a lot of extra money one month. More than my small, low interest loan, but less than my large high interest loan.

If I pay that towards the larger loan, my payments remain the same each month. So I've got the same problem - sometimes I have to eat beans or miss a payment.

Paying off the smaller loan frees up cash. I don't have to eat beans on the bad months anymore.

As other answers have pointed out: In theory, highest interest rate first is the most logical way to handle your debt with all other things being equal.

However, in the real world, not all debts are equal.

• Some debt repayments might come with hidden costs. Annuity loans often come with a fixed repayment rate and modifying that rate or doing a larger down payment might come with additional fees. That can sometimes outweigh the benefit of paying them off earlier. Do the math!
• Some debts might be with creditors who are willing to negotiate. They might be willing to forgive the debt if you pay a part of it now. Or they might be willing to negotiate a lower interest rate. But as soon as the debt is paid off, your leverage in that negotiation is zero. So if you believe that a creditor might still be willing to accept concessions if asked nicely, then that loan would be lower priority until those negotiations failed.
• Some debts might be contestable. Perhaps the debt is not actually valid? A bill for goods or services that were faulty or which you never ordered? A fine even though you did nothing wrong? A court decision says you need to pay compensation, but there is still a realistic chance to appeal it? A clerical error? Someone trying to scam you? If you still see a way to contest such a debt, then paying it off might weaken your position. However, if you fight and lose, then the debt accrues interest in the mean time. So you need to estimate your chance to contest it successfully and do the math to see if fighting it is worth it.
• Some debts might be with creditors who are more annoying than others. You might have some creditors who don't pay much attention to you and other whose behavior borders on harassment. For your personal sanity you might want to deal with the most threatening creditors first. But remember to spread the word about creditors who use such business practices.

Here is Dave Ramsey's succinct explanation:

"Debt is a behavior problem, not a math problem."

https://www.knoxnews.com/story/money/columnists/2019/10/02/dave-ramsey-getting-out-of-personal-debt-snowball-interest-rate-change-behavior-financial-advice/3829382002/

Clearing out the smaller debts seems to provide the debtor with small wins that reinforce the desired behavior of getting out of debt. Mathematically it is of course more efficient to pay off the highest interest debts, but useless if the debtor is not able to modify behavior over the time required to pay off the debts.