When you look to open a savings account or something similar like CDs, you quickly learn that not every bank offers the same interest rate.

Another thing you're bound to notice as you compare options is that some accounts advertise that interest is compounded on a daily or monthly basis, but it may not be clear which is better and how much of a difference it makes in any event.

Fortunately, it's fairly easy to learn these fundamentals of finance.

## What is Compound Interest?

Compound interest is, simply, "interest on interest." But the best way to explain it is with an illustration that compares the different ways interest can be handled.

### Simple interest

Let's say you have a balance of $100,000 in a savings account which pays interest of 3% per year.

If you guessed that you would earn $3,000 in a year, you would be correct. After all, $100,000 times 3% equals $3,000. That is an example of simple interest.

If you withdraw your $3,000 interest at the end of the first year, your remaining principal will be $100,000, the amount with which you started. Your interest the second year at 3% will again be $3,000.

This phenomenon, where the principal stays the same (in this case $100,000), and the interest every year also remains the same, is called "simple interest."

### Compound interest

When the interest is left in the account along with your initial investment, interest is earned both on the principal and on the previously gained interest. This causes the sum of the investment's principal and interest earned to grow at a faster rate.

Using the example above, now let's say you leave the interest in the savings account at the end of the first year. If you do that, its balance at the end of the year will be $103,000.

Because the balance in your account has increased, the interest at 3% for the second year will also grow, in this case to $3,090 and, therefore, your total balance at the end of the second year will be $106,090.

You can easily see that the longer you leave your money in your savings account, the higher your interest will be every year because you'll be earning interest on the interest earned in previous years. That phenomenon, where you earn interest on interest, is called "compound interest."

Compound interest clearly is more attractive than simple interest and, in today's competitive banking environment, it is no surprise that almost all banks offer compound interest on their various savings account products. It's also not surprising to see banks refer to multiple methods of compounding.

## Monthly Compounding

In the example above, interest is calculated - and then added to the principal - at the end of every year. A different way to say that is interest is "compounded annually."

If you see a bank advertising that they compound interest monthly as opposed to annually, what does that mean?

It simply means that, instead of waiting to the end of the year to calculate interest and add it to your account, they do it at the end of every month. So at the end of the first month, your interest would be $250, or 1/12th of the $3,000 annual interest.

After they add the interest of $250 to your balance, the principal at the end of January will become $100,250. You can see the interest for February will be slightly higher, $250.625 to be exact. Interest for every succeeding month will also grow correspondingly. March's will be $251.25, and so forth.

At the end of the year, your total interest will come to $3,041.60 if your bank compounds interest monthly. That's $41.60 higher than the $3,000 compared to the earlier example of annual compounding… a pleasant dinner out for two.

## Daily Compounding

Since the guiding principle behind compound interest is that the shorter the compounding term, the more interest you earn, you would expect daily compounding to provide more interest than monthly compounding.

The difference between annual and monthly compounding is not that big, though, and likewise the difference between daily and monthly compounding will also be minor. (In this case, $3,045.33 vs. $3,041.60.)

The principle carries through: the shorter the interval used for compounding, the higher your interest earned will be.

In practice, keep in mind that, even though a bank or credit union might advertise daily compounding, they rarely add that interest to your account every day. Common practice with both daily and monthly compounding is to add the interest on the last day of every month. To do that, banks offering daily compounding track a hidden balance where the interest is added every day and calculate the daily interest on that "shadow" balance.

## What If My Balance Changes?

Few savings accounts remain static all year long. Whenever you make a deposit or withdrawal on an account with daily compounding, the bank's computers simply calculate the interest earned to that date on the previous balance and then use the new balance going forward.

If interest is compounded monthly and you made a deposit on the 10th of July, the bank calculates interest for nine days at the old balance and twenty-two days on the new balance.

Either way, you earn appropriate interest for the portion of month for the balance you had at the end of each day. Again, although daily compounding is better, the difference between that and monthly compounding are likely to be minor, at least in the current environment where savings account interest rates can be close to microscopic.

It is worth keeping in mind that low interest has not always been the case and, in all likelihood, will not remain the case indefinitely. In the 1980s, for example, it was not uncommon for savings accounts to earn 7% interest and higher.

## APR vs. APY

If you were concerned that calculating your yields at various compound-interest terms might be too daunting, don't worry. The banking industry has made it easy for you to figure out your best yields.

APR, which stands for "Annual Percentage Rate," is the interest rate used as the foundation for all the calculations. In the example above, that would be the 3%.

APY, or "Annual Percentage Yield," takes the total interest earned during the year, with all the compounding and its terms factored in, and then calculates it as a percentage of the originating principal.

If you take the $3,041.60 total interest for the year from the monthly compounding example above as a percentage of your originating principal of $100,000, the APY comes to 3.04%.

The APY for daily compounding likewise comes to 3.05%.

Of the two rates, APY is the more revealing, because it shows the effective rate of interest you would receive on your savings, assuming that you leave it untouched for a year. Because it is usually the higher of the two rates, banks love to quote it when advertising their interest rates for savings products like savings accounts, CDs, and money market accounts. Likewise, sites which compare different banks' yields are also likely to focus on APY yields. Therefore, the number to look for when comparing different banks' savings account interest rates is their APY number.

## Conclusion

Compounding interest is a key concept in understanding wealth-building. It can boost your savings if you understand it and take advantage of it. You don't have to know all the mathematical equations behind it to grasp the basic idea.

Three things can influence the rate at which money compounds in an account:

- The APR interest rate earned on the investment: The higher the interest rate, the stronger the rate of compounding.
- The length of time you leave your money in the account to compound its interest: The longer you let your money sit uninterrupted, the larger the returns will be.
- The compounding frequency or the number of times per year in which the accumulated interest is paid out.

Daily compounding beats monthly compounding. The shorter the compounding period, the higher your effective yield is going to be.