Is it better to pay off a loan with a higher interest rate or one with a much higher principal balance?

Question

Okay, we'll start off with some backstory. I went to a for-profit university with absolutely no financial assistance, so now I'm in a very large amount of debt. I've read almost everyone on this site suggests to pay down the loans with the higest interest rate first, for the most part as a hard and fast rule.

As it stands right now, I'm doing just that. But now I'm thinking towards the future. When I pay this one off I'm going to need to choose which of the other loans to hammer down and I'm having some trouble deciding. It breaks down like this(round numbers for easy math):

Loan A: Principal balance of $50,000 Interest: 3%
Loan B: Principal balance of $15,000 Interest: 5%

Based on the "Pay the highest interest rate first" rule, I should be paying down loan B first, but that doesn't make much sense to me; loan A is accruing more interest every month. Am I correct in assuming that I should be paying down loan A first, or is there more long term math that I'm missing out on? Thanks!

Answer 1

You should definitely pay down Loan B first.

Usually this is trickier because the higher balance is also the higher interest rate, so the dilemma is whether to use the snowball method or not.

To summarize briefly, the idea of the snowball method is to pay down smaller balances first, because it feels more successful and therefore makes it more likely you'll stick with it. The amount being paid toward the smallest balance then gets added to the minimum payment of the next smallest balance once the smallest is paid off (this is where the "snowball" name comes from, the payments get bigger and bigger as you finish smaller balances).

In this case, the mathematically better option and the psychologically better option are one in the same.

The reason the math works better is because every $1 you put toward the higher interest rate saves 5% of $1 ($0.05) vs 3% of $1 ($0.03).

The fact that the dollar amount in interest is higher on the larger balance is irrelevant here. Loan A is accruing more interest in total dollars per month, but Loan B is accruing more interest per dollar per month.

Answer 2

If it makes it easier for you to understand, think of it as 65 loans of $1000 each. If you can cover the interest on all of the loans and you have $1000 extra each month to pay, which would you eliminate first? One of the 15 loans that cost more or one of the 50 loans that cost less? What would you do one month from now?

Yes, you are accruing $125 of interest on the $50,000 loan, but if you pay it down by $1000, that will only save you $2.50 in interest next month. The $15000 loan on the other hand only accrues a total of $62.50 in interest each month, but paying it down by $1000 saves you $4.17 in interest next month.

Please note that these numbers reflect simple interest compounded annually, and the actual numbers will be different depending on the details of your loan. I used simple numbers to illustrate the point with your own simple numbers.

Answer 3

You can model this, in an Excel spreadsheet, for example. If I do this, I see a little more than $77,000 to pay off the two debts you mention above (assuming a 10 year loan).

Assuming an extra $200 per month applied (to the mentioned loan first, then the other): If you pay off the $50,000 3% loan first, you end up paying just over $74,100 total. If you pay off the $15,000 5% loan first, you end up paying less than $73,500 total.

Not a huge difference, but I wouldn't argue with an extra $600, even amortized over eight or so years (that extra $200 takes almost two years off the overall lifetime of the loans).