## Interest

Interest is the amount you must pay over time for a loan. Banks pay interest to their depositors, who are in effect loaning the bank their money. Certificates of Deposit pay interest for the same reason, but usually at higher rates because they are in large denominations and withdrawal is restricted. The rate of interest that is most often quoted in these situations is annual percentage yield (APY), or the percent of the original loan principal that will be paid as interest after 1 year. From this base rate, daily and other periodic interest rates can be calculated.

## Calculating Daily Interest Rate on Simple Interest

The very simple process of calculating periodic interest rates from an annual percentage rate is to divide the annual rate by the number of periods. Thus, to find the monthly rate, divide by 12. Divide by 365 for the daily rate. So, if a savings account yields 2 percent annually, this amounts to a daily periodic interest rate of about 0.005479452 percent, the quotient of two divided by 365. Some banks or financial institutions will use a quotient of 360 instead of 365, so be sure to ascertain the actual rate basis when calculating real-world daily periodic interest rates. This simple method, however, only works for simple interest. The calculation is a little bit more complex if the interest is compounded.

## Calculating Daily Interest Rate on Compound Interest

Compound interest means that interest is added to the principal after each period, and therefore accrues additional interest. Interest payments on savings accounts and some CDs is compounded at a regular rate. Transforming an annual interest rate into a compounded daily periodic rate is done through the equation at left, where r1 is the annual interest rate, n1 is equal to one, r2 is the daily periodic rate and n2 is the number of compounding periods in a year (either 360 or 365). If interest is compounded daily, the 2 percent annual rate quoted in the previous example increases to 0.005534246 percent on a daily periodic basis of 365.