Question: Well, I didn’t think not pursuing into Calculus would hurt my home budget skills. Was I wrong…? Please forgive if the x-post to sci.math seems inappropriate.

Here’s the deal. My wife and I, between us, have a few debts. Nothing we can’t handle – a couple student loans and a car loan. The problem is, I want to figure out the “optimum” way to disperse our “loan-paying-back” budget category across our loans. This way, we get the most “bang” for the bucks we can afford to spend. (i.e., when the loans are all paid, we’ve spent – in total – the minimum possible for some given outlay per-month.)

This SHOULD be easy.

Perhaps I’m just being silly, but it doesn’t seem very easy to find the general rules to follow. I’ve beat Excel nearly senseless trying to elicit them, though. (I have been using a somewhat brute-force method of trying to “discover” the relationships, whereas it’s clear that a “more mathematical” approach would be to do the symbolic math out. Unfortunately, I don’t seem up for this at all, at all.)

For any given two (let’s keep it simple) loans, I’ve proven (to myself, not to a mathematician ) that IF they have the same interest rate, the optimal division of the $ to spend on them is in the same proportion as the amounts on the loans themselves. Interestingly, this also makes it so that they will be paid off at the same time (within a month, keeping in mind that any extra at all after the payments goes into the next month.).

Ok, so I tried to find the next rule for the “other” simple case. If I’ve got two loans with DIFFERING interest rates, but the same principle. This I’m finding remarkably difficult to do. I’ve used Excel to generate several test cases. For instance: for a loan of 4% and another loan of 8%, it seems that 60% of the available funds should go to the 8% loan, the rest to the other. (actually 60% – 61%, it’s not quite clear due to some choppiness in my calculations, since they are fairly accurate in modeling the “monthly payment” scenario)

My approach was to try to find out the above “general principle”, then go about trying to join the “interest-rate-different” and “principle-different” cases into one easy-to-use model that I can apply to any two loans.

So far, I’m stuck on finding this equation. I can make big, ugly spreadsheets that basically try out a bunch of cases, look for a trend (using a graph), and narrow down to find the best case for any given scenario, but this really really takes longer than it should.

Can anyone help? Given the commonplace nature of having more than one debt, this must have been done before countless times before, right?

Answer: It is easy enough that it becomes hard! The answer is always to pay off the highest interest rate loan fastest. This means, if there are multiple loans with different interest rates, pay the minimum on all but the highest-rate loan, and pay everything else to that loan. When it is paid off, move to the next highest. If there are several tied for the highest, it doesn’t matter if you split evenly or unevenly.

There are a few other complications if these aren’t actually “loans” but are lines of credit or credit cards:

* Annual fees should be calculated as a part of the interest rate unless you plan to keep them after paying it off.

* Bonuses based on balance (such as AT&T Universal’s new program) should be calculated as credits on the interest rate if you plan to use them (based on your value).

* The harder calculation is when to transfer balances from one account to another. If there is no fee, it is simple — do it whenever you can transfer to the lower-rate account. With a fee requires more calculation.

And, of course, don’t forget that you’ll pay of that last loan very quickly since you’ll pay the entire month’s payments towards one loan.

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