If you're familiar with Dave Ramsey, then you've no doubt heard of his 'snowball' approach to paying down your debt. In short, Ramsey suggests that you make minimum payments on all but the debt with the lowest balance. Once the low-balance debt is paid off, you add the dollars that had been going there to what you've been paying against the next lowest debt. And so on. The idea is to pick up steam in paying down your debts by knocking them out one by one, and piling up the payments that would have gone to each of the paid off debts in order to knock out the next one. Sounds enticing, but is it a good idea?

To my mind, what you should really be doing is paying down the debts with the highest interest rate, regardless of balance. It just makes intuitive sense to pay off the most costly debts first. Once the debt with the highest interest rate is paid off, add those dollars to what you've been paying on the debt with the next highest interest rate, and so on. So who's right?

I was actually inspired to look into this in greater detail by a recent post over at the Wealthy Blogger. In that post, Mike introduces yet another approach. As outlined in The Automatic Millionaire, this approach is based on the ratio of the outstanding balance to the minimum amount do. Divide the latter into the former, and concentrate your payments on the debt with the lowest resulting value. Once that's paid, add the dollars that had been going there to what you've been paying on the debt with the next lowest ratio. Lather, rinse, repeat. Again, sounds like it might be a good idea. So let's look deeper.

Consider a family with the following debts:

Visa ($7,500 @ 13%, minimum payment = $150/month)
MasterCard ($10,000 @ 19%, minimum payment = $250/month)
Car Loan ($5,000 @ 8%, minimum payment = $275/month)

Note that I essentially picked these values out of thin air.

Now, let's first consider what happens when you make only the minimum payments month after month:

Visa:
Months to pay in full: 72
Total amount paid: $10,685.54
Total interest paid: $3,185.54

MasterCard:
Months to pay in full: 63
Total amount paid: $15,544.23
Total interest paid: $5,544.23

Car Loan:
Months to pay in full: 20
Total amount paid: $5,310.14
Total interest paid: $310.14

So it would take a grand total of 72 months and $31,539.91 to pay off the initial $22,500 in debt. Not too good.

Now let's assume our hypothetical couple can actually afford to pay $1,000 per month toward their debts, rather than just making the minimum payments. What's the best way to allocate these dollars? According to Ramsey, they should attack the car loan first, since it has the lowest balance. In other words, they'll be paying $150/month toward their Visa bill, $250/month toward their MasterCard, and the balance ($600/month) toward the car loan. Using this approach, the car loan gets paid as follows:

Car Loan:
Months to pay in full: 9
Total amount paid: $5,126.70
Total interest paid: $126.70

At that point, the next highest balance is the Visa, so they add the $600/month from the car loan to the $150/month they already been paying, and they finish off the Visa.

Visa:
Months to pay in full: 19
Total amount paid: $8,477.38
Total interest paid: $977.38

And from this point on, the entire $1,000 gets poured into the MasterCard until it's gone.

MasterCard:
Months to pay in full: 27
Total amount paid: $13,013.74
Total interest paid: $3,013.74

So it's all done in 27 months at a cost of $26,617.82. That's a net savings of 45 months and $4,922.09 in interest payments. Not too shabby. But could they do better?

Let's look at what would happen if they hit the highest interest rate first. In this case, they'd attack the MasterCard, Visa, and car loan, in that order. The result? The MasterCard ends up as follows:

MasterCard:
Months to pay in full: 20
Total amount paid: $11,572.27
Total interest paid: $1,572.27

Coincidentally, due to the lower initial balance, the car loan ends up getting paid off during that same month, even thought they've only been paying the minimum amount each month.

Car Loan:
Months to pay in full: 20
Total amount paid: $5,310.14
Total interest paid: $310.14

So now the whole ball of wax gets applied to the Visa, wiping it out as follows.

Visa:
Months to pay in full: 26
Total amount paid: $9,093.73
Total interest paid: $1,593.73

So they're out of debt in 26 months at a total cost of $25,976.14. That's a month sooner, and they've saved an additional $641.68.

What about the approach advocated in The Automatic Millionaire? In this case, the car loan has the lowest initial ratio (and it turns out that it remains lower until it's paid in full). Thus, as with Ramsey's approach, our hypothetical couple starts out hitting the car loan the hardest, at $600/month.

Car Loan:
Months to pay in full: 20
Total amount paid: $5,126.70
Total interest paid: $126.70

At that point, the MasterCard has the lowest ratio (and it remains lower than the Visa until it's paid off). So they switch to paying $850/month on their MasterCard and continue paying the minimum on their Visa.

MasterCard:
Months to pay in full: 21
Total amount paid: $12,052.55
Total interest paid: $2,052.55

And now it's time to kill off the Visa.

Visa:
Months to pay in full: 27
Total amount paid: $9,114.65
Total interest paid: $1,614.65

Thus, in this case, the more convoluted, ratio-based approach takes the same length of time as Ramsey's approach, although the remaining payments in that final month are slightly lower, bringing the total to $26,293.90. This is a savings over Ramsey's approach of $323.92, owing to the fact that the vagaries of the numbers that I picked to start with resulted in the high-interest MasterCard getting attacked before the Visa.

The bottom line...

Snowball: 27 months; $26,617.82
High interest first: 26 months; $25,976.14
Automatic: 27 months; $26,293.90

If you work through the math, the best you can hope to do (in this specific case, as well as in any other) is to attack the highest interest rates first. In some cases, Ramsey's approach will equal this approach (if lowest balances are on highest rate debts then the two approaches are the same), but it will never exceed it. Similarly, the approach advocated in The Automatic Millionaire will, in some cases, equal the performance of the high-rate approach – but only if the ratios work out such that the highest rate debts get paid first. But, like the 'debt snowball,' this approach will never beat the high-rate strategy.

With regard to Ramsey's approach vs. the Automatic approach, the relative performance for any given scenario will depend on the numbers. In some cases, Ramsey's approach will do better, in others it won't.

I should note here that, although the numerical differences in this particular example aren't that huge, they can work out to be pretty sizable depending on the amount of debt involved and the structuring of the interest rates.

This isn't to say that an approach such as Ramsey's isn't worthwhile. For example, under Ramsey's scheme, the first debt gets knocked out very quickly, and some people may need that psychological boost to keep at it. In contrast, it took twenty months to knock out the first debt under the high-rate scenario, although two debts (MasterCard and car loan) ended up getting knocked out that same month.

From my perspective, though, Ramsey is doing his followers a disservice by ignoring a method that could save them even more money.

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"Dave Ramsey is Bad at Math" was first published at fivecentnickel.com