We often hear that Albert Einstein called compound interest the eighth wonder of the world. We don’t actually know whether or he actually said that or not, but we do know that compound interest is extremely powerful. When you have compound interest on your side, it’s easier to build wealth. The downside, of course, is that having compound interest working against you can be frustrating and keep you from reaching your financial goals.
Here’s what I mean. It’s much better to earn interest than to pay it, and that’s especially true when you’re talking about compound interest.
What is Compound Interest?
When talking about interest, we’re talking about the right to have a share in something. If you buy a stock, you have an interest in the company — you have a piece of ownership. When someone lends you money, they have a right to get that money back. They have a legal share in what you earn going forward, since you’ve agreed to repay the loan.
In terms of debt, interest is basically the surcharge for getting access to capital. If you borrow money, you’re accessing capital you wouldn’t normally be able to get. Whoever provides you with that capital wants to make money on the deal, and so charges interest.
You can earn interest, though, by letting your own money be used by others. Investing in stocks, or putting your money in a savings account, are examples of ways that you offer up money to be used by others. In return for letting others use your capital, you are paid interest.
There are two types of interest:
- Simple interest is interest paid on the principal capital only
- Compound interest is paid on the principal, plus the accumulating interest
Basically, compound interest is how your money makes money on your behalf. If you invest, it means you not only earn a return on the initial amount of your investment, but also earn a return on your earnings.
On the flip side, though, it also means that if you borrow money, you’re charged interest on your interest. This is seen especially with credit cards that compound interest on a daily basis. At the end of each day, a credit card will look at your balance, figure out how much interest you should be charged, and then add that interest charge to the balance. The next day’s balance now includes your latest interest charge — and your new interest fee will be figured using the new total balance.
How Compound Interest Works
Compound interest is most powerful over time. The longer you put your money to work, the bigger the results. Of course, this also works the same way with debt. The longer you carry debt, particularly credit card debt, the more you end up paying.
Below is the compound interest formula, which allows you to see how it all breaks down. (You can see more examples from DePaul University.)
A = The amount of money accumulated, including interest. This is what a loan will cost you over time, or what you have the potential to earn with an investment, depending on whether you’re paying interest or earning it.
P = The principal.
r = The annual interest rate, represented as a decimal.
n = The number of times the interest is compounded each year (so daily compounding would be 365)
t = The time involved, in years.
Let’s look at why compound interest can be so devastating when you carry a credit card balance for a long period of time. If you have a credit card balance of $5,000, and the annual rate is 17.99% compounded daily, and you carry that debt for five years, the amount that you would pay over all is:
A = 5,000 (1 + (0.1799/365))^(365)(5) ≈ $12,289.14
As you can see, carrying credit card debt for a long period of time can be expensive. However, this formula only shows you the final amount if you weren’t paying down the card. Over time, you would pay down the credit card, and not actually end up pay that full amount. But it’s a good illustration as to why you should avoid paying compound interest if you can.
Earning compound interest is a much better prospect, and you can really see how time matters when you look at it from this standpoint. If you have $10,000, and you put it in an S&P index fund with annualized gains of about 7% per year, compounded quarterly, and you let it grow for 30 years, this is what you would end up with:
A = 10,000 (1+(0.0700/4))^(4)(30) ≈ $80,191.83
That’s not bad, for just letting your money sit there, earning on your behalf. If you let it go for 40 years, though, you end up with about $160,511.76. That’s twice as much, just for letting your money sit for an extra 10 years. You can see what a difference compound interest over time makes!
Of course, you get better results from compound interest if you make regular additions to your account. If you go to Money Chimp, you can see that the formula for annual additions is:
Balance(Y) = P(1 + r)Y + c[ ((1 + r)Y + 1 – (1 + r)) / r ]
This assumes that you make an addition at the end of each year. You can get a pretty good idea of what you could do with the help of dollar-cost averaging, though, using this formula (or just doing yourself a favor and using a handy compound interest calculator found online).
My son, for example, opened a Roth IRA this year for the earnings he has from working in my home business. His annual addition is going to be quite small to start, about $300 for the whole year. But he’s 12. So if he makes contributions for the next 50 years, that $300 a year ($25 per month), compounded quarterly, has the potential to end up as $135,740.28. That’s pretty powerful. And, of course, he’ll increase his contributions as he gets old (I hope).
Consider an average worker. If you’re 25 and you set aside $450 a month (compounded quarterly) for the next 40 years (to retire at 65), you will have a nest egg of $1,181,409.83. If you start at age 35 and want to retire in 30 years, at age 65, that $450 a month is only going to amount to $550,955.76, assuming a 7% annualized rate. With compound interest, a 10-year difference can mean retiring as a millionaire (or not).
As you can see, compound interest can, indeed, be a big deal. You want to be the one earning compound interest, NOT paying it. If you want to be successful in the long run, put compound interest to work on your side, rather than paying that interest to someone else.
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