The Debt Math Throwdown (or testing the debt snowball)

In my discussion about how to pay off your debt, I mentioned how there were primarily two schools of thought: pay off the highest interest rate first, or pay off the smallest debt first (a.k.a. “the debt snowball”).

The debt snowball camp points to the psychology of the method as ensuring its success. The highest-interest-rate camp points to how you will spend less with this method (and thus pay off your debts sooner).

As a fan of the debt snowball, but a fan of spending less, I was intrigued to figure this out. Because it’s not enough to say “you will spend less.” I say: how much? $5? $500? $5,000? The word “less” is nebulous; just like people say that travel is “too expensive”. I’m a math guy; I want numbers! After all, a known quantity can be compared more easily than an unknown quantity.

Looks like it’s time for a Debt Math Throwdown.

Keep it clean

Some ground rules. It goes without saying that every debt situation is going to be different and therefore each situation has to be judged on its own merits. But in general, I think we can take the following to be a good representative sample of a debt situation.

Consider the following debts:

• Personal loan: $20,000 @ 15% ($400 minimum monthly payment)
• Credit card: $10,000 @ 10% ($200 minimum monthly payment)
• Student loan: $8,000 @ 5% ($100 minimum monthly payment)

Let us also say that you have allocated $800 to spend per month on debt. With $700 in minimum payments, you start with an extra $100 to allocate.

Ready…set…go!

WARNING: Dramatic Math ahead (If this troubles you, feel free to skip this section.)

Contestant #1: Snowball

Snowball’s plan involves paying off debts in the following order:

1. Student loan
2. Credit card
3. Personal loan

Snowball starts out allocating $400 to the personal loan, $200 to the credit card, and $200 to the student loan (the minimum plus $100 extra). At $200 per month, it will take 44 months to pay off the student loan, paying about $8,770 total, or $770 in interest.

Meanwhile, Snowball moves over to the credit card which, after 44 months paying the $200 minimum, is down to a balance of $3,800. Snowball now allocates the $200 dollars freed up from the student loan to the credit card, so now paying $400 a month. At that rate, it will be 10 more months until the credit card is paid off.

Now, 54 months in, Snowball allocates all $800 to the personal loan (which at this point is down to $8,500). At this rate, it will take only 12 more months to pay off this final loan and be done.

Totals:

• Total time: 66 months
• Interest paid from personal loan: $9,625
• Interest paid from credit card: $2,805
• Interest paid from student loan: $770
• Total interest paid: $13,200
• Total paid: $51,200

And now we try the other way…

Contestant #2: Interest

Interest’s plan involves paying off debts in the reverse order from Snowball:

1. Personal loan
2. Credit card
3. Student loan

Interest starts out allocating $500 (the minimum plus $100 extra) to the personal loan, $200 to the credit card, and $100 to the personal loan. At $500 per month, it will take 56 months to pay off the personal loan, paying about $27,900 total, or $7,900 in interest.

Meanwhile, Interest moves over to the credit card which, after 56 months at $200 is down to $1,600. Interest now allocates the $500 dollars freed up from the student loan to the credit card, so now paying $700 a month. At that rate, it will only take 3 months until the credit card is paid off.

Now, 59 months in, Interest allocates all $800 to the student loan (which at this point is down to about $3100). At this rate, it will only take 4 more months to pay off this final loan and be done.

Totals:

• Total time: 63 months
• Interest paid from personal loan: $7899
• Interest paid from credit card: $2941
• Interest paid from student loan: $1483
• Total interest paid: $12,323
• Total paid: $50,323

Recap

So Interest clearly paid less money ($50,323 versus $51,200) and paid off the loans sooner (63 versus 66 months).

But the difference isn’t all that much. Snowball was only three months behind Interest, and only paid $877 dollars more. That is $14 dollars a month difference, or 1.7% of the total amount paid.

And what did Snowball get for that extra money? Snowball paid off the first debt one year sooner than Interest. Snowball notched a success on the board while Interest was just plugging away.

That is not insignificant. When you knock something off your list, you’re going to feel like you’re making progress. That extra year before that success could be the difference between making it work and getting discouraged.

And this situation had a number of debts that were all relatively high. Many people have debts that are small, and therefore can be knocked off much sooner, giving that confidence boost (and simplification) much sooner as well.

Now, this is only one situation, so I encourage you to do a similar analysis. If you’re considering going with the higher interest-rate first method because you hear that you will spend less, it is true, but not by much at all. So I stand by my original conviction: better to go for the quicker wins and use the debt snowball.

(If anyone is interested in seeing the spreadsheet where I calculated this out, please contact me and I’ll be happy to share it.)

But enough about me. Do you ever make these kind of calculations when making plans? I can’t be the only one, right?