The "power of compound interest" is a common refrain among personal finance experts, and compounding really can be powerful stuff, because instead of just earning interest on your money, you earn interest on the interest. The more often a savings account compounds, the better, but when you run the numbers, you find that the difference between an account that compounds daily and one that compounds semi-annually isn't all that big.

## Compound Interest

With compound interest, the interest you earn on your money gets added to the principal, which in turn earns more interest. Say you had $10,000 in some sort of account that paid 4 percent interest once a year. After one year, you've earned $400, and your new balance is $10,400. The next year, you earn 4 percent of the new balance, or $416, and your new balance is $10,816, and so on, with the balance growing each year. Contrast this with "simple interest," in which you earn interest on your money, but that interest doesn't get added back into the principal. In this example, you'd just get $400 every year. Under compound interest, it would take about 19 years to double your $10,000. With simple interest, it would take 25 years. That's the power of compound interest.

## Compounding Schedules

Every savings account that compounds your interest has a "compounding schedule." This refers to how often the bank actually credits your account for the interest you've earned. Under a daily compounding schedule, as you can guess, the bank does it every day. So every day the principal grows by a tiny amount, and that tiny amount begins earning interest on its own immediately. Under a semiannual compounding schedule, the bank does it only twice a year. Every year on, say, January 1 and July 1, the bank dumps six months' worth of interest into your account, where it can begin earning interest on its own.

## Compounding vs. Accrual

At this point, daily compounding probably seems preferable to semi-annual compounding -- and it is, but not by as much as it looks at first glance. That's because "compounding" refers only to when the bank deposits interest into your account. The way it calculates the interest you've earned is a separate issue, called accrual. Bank accounts calculate your interest earnings every day, keep track of them, then deposit them in your account according to the compounding schedule. Say you have $10,000 in a savings account that earns 1.5 percent annual interest. Based on a 365-day year, your money earns 0.0041 percent interest every day. After one day, the "accrued" interest is 41 cents. With a daily compounded account, that amount immediately gets added back to your principal, so your new balance is $10,000.41. But with a semi-annually compounded account, your balance remains $10,000, with the 41 cents set aside until the next compounding time -- up to six months in the future. The next day, each account again earns 0.0041 percent interest. The daily compounding account, because it has 41 cents more in it, earns more interest -- 0.0041 percent of 41 cents, to be exact, or a whopping 0.0017 cents more. Over time, those fractions of a penny get bigger, and they add up.

## The Real Difference

After a full year, a $10,000 balance in a savings account that pays 1.5 annual interest will have grown to about $10,151.13 under daily compounding. Under semi-annual compounding, the balance will have grown to about $10,150.56. The difference: roughly 57 cents. Not exactly a down payment on a house, but real value, nevertheless. People make decisions every day -- at the grocery store, for example -- on the basis of even less money. Of course, in the example, no money was added to or withdrawn from the account over the course of the year, but it really wouldn't have made a major difference, since interest would have still been accruing daily under each compounding schedule. Bottom line: The more often a savings account compounds, the better, but you may not see much of an effect unless you have six figures in the account. Also, when shopping around for accounts, don't just ask how often an account compounds interest, but also the rate at which it accrues interest.