# Formula for how to distribute a loan payment between multiple loans such that the remaining principal accrues the least interest?

Assume 4 loans (Balance @ p.a. interest):

1. \$10,000 @ 5.5%

2. \$5,500 @ 7.25%

3. \$2,000 @ 5.5%

4. \$1,000 @ 4.5%

If I am looking to pay \$7,250 towards principal only, how would I calculate the amount of money to pay towards each loan such that it would leave me with the lowest possible accrued interest next month?

• You do mean annual interest rate not monthly interest rate? Jul 28, 2014 at 21:26
• @Victor That is correct, although it wouldn't change the outcome too much? Other than how often the principal is compounded? Jul 29, 2014 at 23:47

I would pay the minimum amounts on all loans then pay off the \$5,500 @ 7.25% (highest interest rate), then pay any remainder on the \$2,000 @ 5.5%.

Even though (1) and (3) are at the same rate, I would pay (3) off first as it is a smaller amount and thus can be paid off sooner - giving you less loans to concentrate on paying off .

• +1 - now I'll brace myself for The David fan to suggest the loans be orders by size, and pay the \$1K & \$2K first, then what's left to the \$5,500 loan. Nonsense of course, but you know it's coming. Jul 25, 2014 at 1:30
• +1 indeed, and for skeptics and The David fanatics, I suggest trying out different payment schedules at powerpay.org to see which one will work best for them. Jul 25, 2014 at 1:55
• Assuming I don't care how many loans I have to track and that the minimum could be \$0 payment; The loan with the largest interest right now would be the \$10,000 @ 5.5%. Basically I want the exact dollar amounts to pay to each loan out of \$7,250 that would make the accrued interest the lowest overall next month. To me it seems that the most bang would probably be something like \$4,500 towards loan 1 and the remainder \$2,750 toward loan 2. I was just curious if there is a formula to enter all your variables into and it would solve the exact dollar amount to maximize your payment. Jul 28, 2014 at 18:46
• If there is no minimum on any of the loans and the terms are all the same, the highest interest rate is number 2. You would pay this one fully off, then could use the remaining \$1750 on either 1 or 3 as they are at the same rate. Personally I would pay off 3 first as then once paid off I would have one less payment to make each month. No formula needed - rule of thumb pay off higher interest first if all else the same. Jul 28, 2014 at 21:22
• @Shawn Sheesh! My previous comment on Victor's answer includes a link to a website where you can play with the numbers for yourself to figure out the best strategy, which, incidentally, is exactly what Victor has told you already. Stop dithering around about what "seems" to you to give the most bang and do what Victor has told you to do. Jul 30, 2014 at 2:19

Ditto to Victor. The simple rule is: Pay the minimums on all so you don't get any late fees, etc, then pay off the highest interest rate loan first.

A couple of special cases do come to mind:

1. If one or more of these are credit cards, then, here in the U.S. at least, credit cards charge you interest on the average daily balance, unless you pay off the balance entirely, in which case you pay zero interest. So for example say you had two credit cards, both with 1% per month interest, with debt of \$2000 and \$1000. You have \$1500 available. Ignoring minimum payments for the moment, if you put that \$1500 against the larger balance, you would still pay interest on the full amount for the current month, or \$30. But if you paid off the smaller and put the difference against the larger, then your interest for the current month would be only \$15. (Either way, your interest for NEXT month would be the same -- 1% of the \$1500 remaining balance or \$15 -- assuming you couldn't pay off the other card.)

2. If one or more of the loans are mortgage loans on which you are paying mortgage insurance, then when you get the balance below a certain point -- usually 80% of the original loan amount -- you no longer have to pay mortgage insurance premiums. Thus the amount you are paying on such premiums needs to be factored into the calculation.

There may be other special cases. Those are the ones that I've run into.

• +1 - Proving once again that nothing is as simple as it might appear. Your first point is well taken. Having one card free and clear in effect provides a zero interest card, so long as that card is always paid in full. The payoff analysis usually assumes \$X/mo till paid off, but not the fact that there are still new charges. Jul 25, 2014 at 16:39
• The tag on the question is student loans. Jul 28, 2014 at 18:34
• @shawn True, and I didn't notice that when I wrote my answer. But the question didn't mention student loans, and in any case, I don't know what the terms are on your loans, they might resemble credit cards, etc, in their terms. If not, then okay, those comments aren't relevant.
– Jay
Jul 28, 2014 at 19:59