When you see a savings account with an interest rate of, say 1%, it looks small. And it is. But thereâ€™s a misconception about how small it really is: people underestimate the power of compound interest.

Letâ€™s start with regular, simple interest. Imagine that you have $1,000 in a bank account that pays 1% interest annually. After a year, the bank gives you 1% of that principal sum, $10, as interest. You now have $1,010. The formula here is: Interest = principal x Rate x Time. That would be $1,000 for the principal, times 0.01 (which is 1%), times 1, for one year.

In addition to earning interest on the principal, compound interest actually allows your interest to earn its* own* interest, which can make a big difference in the long run. In other words, compound interest is the interest you earn on both your original money and on the interest you accumulate.

High-yield savings accounts offered by many online banks pay a 1% interest rate on your money, and pay it every month. But they actually compound interest every dayâ€”365 times a year. That means every little bit of interest gets put to work almost immediately.

The formula calculating the compound interest earnings for that is a little fancier:

**P(1+(r/n))^(nt)-P = I**

But once you plug in some numbers it gets a little better, say $1,000 invested at 1% compounded every day for a year.

**$1,000(1+(.01/365))^(365*1)-$1,000 = $10.05**

The interest accrued comes out to $10.05. OK, so not that much better than simple interest. Itâ€™s only a nickel more.

But when these numbers are bigger, it gets interesting. Make the timeframe 10 years and you get $105.17 in interest earned. Without compounding, youâ€™d have $100.

Now, letâ€™s say you have a 7% interest rate. In 10 years $1,000 brings you to $1,700 with simple interest (without compounding). If you were to have daily compoundingâ€”common in most bank savings accountsâ€”youâ€™d have $2,013. Thatâ€™s almost 20% more thanks to daily compounding over the simple formula.

While you used to be able to invest in an online savings account at high interest rates, you canâ€™t really do that today with the low rates set by the Fed. (However, investing in the stock market has historically yielded an annualized return of about 7%. Stocks donâ€™t pay interest, but they do produce earnings and pay dividends; those earnings get reinvested and can earn even more. The more time your money stays invested, the more opportunity for compounding and growth.)

A handy thing to know when it comes to all of this is the â€śRule of 72.â€ť This rule gives you a pretty good estimate of how long itâ€™ll take for you to double your money, given a certain interest rate. Just take 72 and divide it by whatever your interest rate is to see how many years itâ€™ll take.

This is really helpful at illustrating the value and power of compound interest because it shows that the difference of just 1 percentage pointâ€”say between a 3% and 4% return is the difference of doubling your money in 24 years or 18 years.

Check out some compound interest calculators from the SEC and Bankrate.

*Ethan Wolff-Mann** is a writer at Yahoo Finance focusing on consumer issues, tech, and personal finance. Follow him on Twitter**@ewolffmann**. Got a tip? Send it to tips@yahoo-inc.com.*

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