## Part III – Compound Interest and Consumer Debt

By The Banker | Blog Posts, Inequality, Personal Finance, Uncategorized, Wall Street
14 Feb 2013
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Part III – Compound interest and Consumer Debt

Please see earlier posts Part I – Why don’t they teach this in school  And Part II – Compound interest and Wealth

So in the last post I wrote about the the incredible power of compound interest, and the possibility it suggests about wealth creation over time.

On the debt side of things, how much does your credit card company earn if you carry just an average of a \$5,000 credit card balance, paying, say, 22% annual interest rate (compounding monthly) for the next 10 years?

In your mind you owe a balance of only \$5,000, which is not a huge amount, especially for someone gainfully employed.  After all, \$5,000 is just a quick Disney trip, or a moderately priced ski-trip, or that week in Hawaii.  You think to yourself, “how bad could it be?”

The answer, including the cost of monthly compounding[1], is \$44,235, or about 9 times what it appears to cost you at face value.[2]

I hate to be the Scrooge, but the power of compound interest transformed that moderate credit card balance of \$5,000 into an extraordinarily expensive purchase.[3]

Compound interest: Why the poor stay poor and the rich stay rich

To take another example, let’s think of compound interest on credit cards for the average American household.

Let’s say you are an average American household, and you carry an average balance of \$15,956 in credit card debt.

Also, as an average American household, let’s assume you pay an average current rate of 12.83%.[4]

Finally, let’s assume you carry this average balance for 40 years, between ages 25 and 65.  How much did your credit card company make off of you and your extreme averageness?

So, in sum, your credit card company will earn from the average American household carrying a credit card balance for 40 years, \$2.6 million. [6]

If you’re wondering why rich people tend to stay rich, and poor people tend to stay poor, may I offer you Exhibit A:

Compound Interest.

Now, your math teacher might not have done this demonstration for you in junior high, because he didn’t know about it.  Mostly, I forgive him.  Although not completely.

You can be damned sure, however, that credit cards companies know how to do this math.  THIS MATH IS THEIR ENTIRE BUSINESS MODEL.

Which same business model would work a lot less well if everyone knew how to figure this stuff out on his own.

Hence, my theory about the Financial Infotainment Industrial Complex suppressing the teaching of compound interest.  They don’t want you to learn how to figure out this math on your own.[7]

[1] But importantly, excluding all late fees, overbalance fees or penalty rates of interest.

[2] We get this result using the same formula, although Yield is divided by 12 to account for monthly compounding, and the N reflects the number of compounding periods, which is 120 months.  So the math is: \$5,000 * (1+.22/12)120

[3] Have you ever wanted to take a \$45K vacation to Hawaii and pretend you’re a high roller?  Congratulations!  By carrying that \$5K balance for 10 years, you did it!  You took a \$45,000 Hawaiian vacation. You’re a high roller! Yay!

[4] All of these stats taken from this great site on credit card statistics, which cites all of its sources.

[5] We express this again dividing yield by 12 to account for monthly compounding, and raising it to the power of 480 months, the number of compounding periods.  Hence the math is \$15,956 * (1+.1283/12)480

[6] I’m assuming for the purposes of this calculation that the debt balance stays constant for 40 years, but your household pays interest on the balance.  In calculating this result, please note I have framed the question in terms of “How much does the credit card company earn” off of your household carrying this average balance for 40 years.  Which is not the same question as “How much do you pay as a household?”  Embedded in my assumptions, and the compound interest formula, is the idea that the credit card company can continue to earn a fixed 12.83% on money you pay them.  Which I think is a fair way of analyzing how much money they can earn off your balance.  Since there are no shortages of other household credit card balances for the credit card company to fund at 12.83%, I believe this to be the most accurate way of calculating the credit card company’s earnings on your balance.

[7] Here’s where, for the sake of clarifying sarcasm on the internet – which sometimes doesn’t translate well on the electronic page – I should point out that I’m (mostly) kidding about the suppression of the compound interest formula.  Among the main reasons I started Bankers Anonymous was that the dim dialogue we have about finance as a society allows conspiracy theories to grown in darkness.  Just as pre-scientific societies depend on magic to explain mysterious phenomena, I think financially uninformed societies gravitate toward conspiracies to explain complex financial events.  As a former Wall Streeter who does not actually ascribe to conspiracy theories, I feel some obligation ‘to amuse and inform’ and thereby reduce the amount of conspiracy-mongering.  So, I don’t really think there’s a conspiracy here.  As far as you know.  Or maybe, that’s just what I want you to think.

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Hey Mike, As I have mentioned before, my wife and I have eight children (20 – 32) and non of them have a clue of this subject as it relates to their lives except that three have found a way to get out of credit card debt and do not want to go back there again. Two have gotten a sniff of compound interest after they have purchased cars on time. I am with you as far as your sense that the financing industry despises disclosure. I believe that the two kids that viewed the total pay out information as a result of their car purchase started to get it. Anyway keep up the good work and maybe children at ages earlier than high school can learn to work the HP12C and get it using monopoly money in some form of game.

• The Banker says:

Or I’ll publish the book sometime soon so you can buy it for them!

2. Robert says:

Maybe I’m an idiot but I can’t make the math run on the credit card debt. If I enter 5000 x 1.22^10 it gives me 36,000 odd. What am I doing wrong?

3. Robert says:

Ah shit just realised why I screwed it up. Monthly interest, right?

• The Banker says:

monthly compounding! 5000 * (1.22/12)^120. Divide by 12 because its monthly, raise to the power of 120 because that’s the number of compounding periods. I”m glad you’re working out the math!

4. Robert says:

Thanks! I would have realized from the footnote but my browser doesn’t like the links so I just get a few humourous/informative snippets at the end of each post!

5. Dean Johnson says:

This is highly misleading. The author has the interest rate compound by assuming that the lender makes the same interest rate going forward. Of course, if the borrow pays the interest currently, there isn’t any compounding of the interest, either monthly or for 45 years. This is a slight of hand and very, very deceptive in my opinion. If you pay the interest, it costs you the interest rate times the balance times 45 years. There won’t be any compounding.

• The Banker says:

You’re right that the borrower only pays the interest that he pays. Which is why I phrased it as “This is how much the credit card companies make,” rather than “This is how much you pay.” I think it is fair to assume credit card companies can earn the same interest going forward from other borrowers. But that is open to interpretation and disagreement. So, you’ve made a fair point.