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Say I have a $100k 3% mortgage with min $1k payment, $10k 5% car loan with $100 min payment and $1k 20% credit card with $50 min payment. If I have $1500 to spend, I need to split that to pay back at least the minimum on each loan. A rule of thumb is to overpay high interest first - but that means I pay more interest longer on the bigger loans. There must must be a formula that picks monthly splits to maximize net worth at the end of the payment sequence?

With that formula in hand, I should be able to include investments (flipping the sign on the balance) and optimize savings alongside loans.

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    Does this answer your question? I have 9,000 cash. What debt should I pay first?
    – glibdud
    Commented Jun 16, 2022 at 15:35
  • The rule of thumb minimizes the amount of interest you will pay over the life of all the loans, not the amount of interest you'll pay in one pay period.
    – chepner
    Commented Jun 17, 2022 at 15:48
  • This optimal loan payback problem, at least in a simplified version, could be formulated as a linear optimization and a short script could give you the optimal payment sequence. But the result will only be optimal with respect to the specific way it is defined (and a few parameter changes might give you very different results) so it might be worse than the rule of thumb given in this stack exchange. Nonetheless, if you are interested in the mathematical solution itself you can ask that in Operations Research Stack Exchange or Stack Overflow.
    – jDAQ
    Commented Jun 17, 2022 at 19:34
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    @jDAQ If the result is worse than the rule of thumb, then surely it is not optimal and so would not be the result in the first place. I also think "a few parameter changes might give you very different results" is a surprising claim; do you have a simple example?
    – Daniel Wagner
    Commented Jun 17, 2022 at 20:33
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    This is a good, although common, question, and the answers below are correct. The "rule of thumb" for paying the higher interest rate first is more than just a guideline-- the math backs it up. Using only the loan amounts, durations, and interest rates (ignoring any other factors such as fees, taxes, and psychology), the path that results in you having the most money at the end of the day is by prioritizing the highest interest rate, regardless of duration and amount. That being said, the linked question by @glibdud above is worth reading.
    – elmer007
    Commented Jun 17, 2022 at 20:37

2 Answers 2

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A rule of thumb is to overpay high interest first - but that means I pay more interest longer on the bigger loans.

If you're dealing with fixed rates it's always most efficient to pay off the higher effective interest rate first, regardless of loan duration. Every extra dollar you pay toward either loan is a dollar you don't pay interest on again, so the only question is how much interest will that dollar of debt cost you.

The minimum payment is based on the loan duration, but otherwise loan duration has no impact on deciding what to pay of first.

A thought experiment that some have found helpful is to imagine that instead of having two loans that you have 110,000 loans of $1 each. 10,000 of those at 5% and rest at 3%. They are all one year loans that renew for another year if they go unpaid. Each 5% loan costs you $0.05 per year (simple interest), and each 3% loan costs you $0.03 per year. So every $1 you pay toward a 5% loan saves you $0.05, but that's a dollar you couldn't pay toward a 3% loan, which costs you $0.03, you still save $0.02 per year per dollar put toward 5% loan(s).

Effective interest rate is important because if there is a tax advantage to some debt it could create a preference between two otherwise comparable rates. Not likely an issue in your case unless you were already itemizing deductions for other reasons. I'm also assuming no prepayment penalties.

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    The savings are completely offset by the mental energy used to calculate this. The real savings are extremely trivial, but I'll bet you 2 loans are substantially easier to deal with than 3.
    – Nelson
    Commented Jun 17, 2022 at 8:47
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    @Nelson while typically true, the OP did ask to optimize savings, not simplify thinking. This answer gets right to the heart of the question.
    – GOATNine
    Commented Jun 17, 2022 at 14:24
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    @Nelson Things could get complex if you care to calculate effective interest rates for each debt or have variable rate debt cliffs coming up. The majority of people don't itemize deductions and can just ignore anything beyond "highest rate first" and come out best. Number of loans is irrelevant, that's the point, OP's 2 loans or 110,000 $1 loans makes no difference, pay highest interest rate debt first.
    – Hart CO
    Commented Jun 17, 2022 at 14:28
  • I might suggest adding that-- in addition to the duration-- the loan amount also does not affect the results of the math which shows that paying the highest interest rate first is the most efficient. The 1st and 2nd paragraph only explicitly mention the duration, and the thought experiment doesn't quite make it obvious since the loans are all $1. I find that this sometimes surprises people, since the total interest amount of a larger loan seems to be a factor here, when it isn't (mathematically, ignoring other factors.)
    – elmer007
    Commented Jun 17, 2022 at 20:27
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Hart is absolutely right about paying the highest rate first. Sometimes if the rates are close I'd suggest paying the lowest balance first (to get it knocked out), but your lowest balance happens to be your highest rate, so that's taken care of either way.

However, I wanted to address this:

With that formula in hand, I should be able to include investments (flipping the sign on the balance) and optimize savings alongside loans.

The problem with investing while paying off debt is that you're effectively borrowing money to invest. The interest you pay on the loans is fixed, but the return you get on your investments is variable, and can go negative (as it has this year). Plus there are psychological factors that make it so that you end up paying on debt much longer than you should.

I know several people who borrow to the hilt so that they can max out their investments (thinking they'll earn more than they spend in interest), and they are constantly stressed over the market. An alternative (which I have done) is to prioritize debt, get everything paid off except the mortgage, then focus on investing (and other savings). You'll have more money in your budget to invest and will have no trouble making up for lost time after the debt payments are gone.

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  • If the OP is interested in learning more about this part of the question, maybe consider adding a reference to "leverage" as a term they can search and learn more about. I think we're probably in agreement about what their conclusion should be, though: very risky, proceed with caution, especially if their current lifestyle has resulted in having debts with 20% interest.
    – elmer007
    Commented Jun 17, 2022 at 20:52

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