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Comment by xyzzyz | Hacker News Reader

>Clearly the optimal strategy is to pay off the debt with the highest interest rate first.

Clearly? This is plainly wrong. Let's say we have two debts: $1000 with 0.7% interest rate and $40 with 0.8% interest rate (these rates are daily). Assuming our daily salary is $19, having payed off $40 debt first, we will never be able to pay off the $1000, as the interest exceeds our salary. The other way around, we pay off $1000 (then $2546.5) debt after 135 days, and then a week later we pay off $40 (then $128) debt.

It is not the sole interest rate, but the ratio between interest rate and debt that matters.

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Huh?

    Start: $40 @ 0.8% ($0.32 daily) + $1000 @ 0.07% ($7 daily)
    day 1: pay $19 on the small debt; $21.32 remain (and $1007 on the other)
    day 2: pay $19 on the small debt; $2.49 remain (and $1014.05 on the other)
    day 3: pay off the small debt ($2.51) and pay $16.49 on the remaining one ($1004.66 remain)
    day 4..n: pay $19 on the remaining debt
       balance goes as X=X*1.007 - 19; paid off in 67 more days

Perhaps it would help instead to think of them as investment opportunities: opportunity A pays 0.8% and has a limit of $40 invested, opportunity B pays 0.7% and has a limit of $1000 invested. First you max out opportunity A, then you start putting money into opportunity B. Ignoring opportunity A means you miss out on up to $0.04/day.

Your math is wrong, and I don't think it's possible to fix it and get the conclusion you want (because you should think about your total debt, and how much it goes up each day, when figuring out if you can keep up or not).

The daily interest on $1000 with 0.7% interest is around $7. Waiting a few days to pay of the smaller debt will not make it exceed $19.

Edit: Were you banning partial repayments? Most debt (I think) is not like that, but maybe it makes your math work

> Edit: Were you banning partial repayments? Most debt (I think) is not like that, but maybe it makes your math work

It does make it work assuming that partial repayments are not allowed, and interest is added to the principal (and paid off at the end) instead of being paid as it comes due. I don't think either of these is realistic, especially the second one. Also if I assume a savings account paying even 0.1%, it goes back to being payable in either order.

>Were you banning partial repayments?

Yes, I were. If partial repayments are allowed, it is indeed the best approach.

>The daily interest on $1000 with 0.7% interest is around $7. Waiting a few days to pay of the smaller debt will not make it exceed $19.

Of course not, but they will exceed $19 before you will be able to pay it off as a whole -- it will take more than 130 days.

Maybe I should make my statements clearer, so that next time I do not get downvoted for being misunderstood.

You skipped the Zero-th step:

Step 0: pay your minimum on all debts.

That prevents your principle amounts from increasing

Letting the principal on low interest debt increase in favour of paying off a high interest bearing one earlier, is actually a good idea financewise.

presuming, of course that you can do so without penalty, yes. But there are very few source of credit which will let you get away with deferring payments penalty-free.

That's an interesting boundary case, but you are arguing the proper way to pay off a debt for someone who is clearly in a bankrupt situation.

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