If you buy a certificate of deposit or open a savings account, the bank states the annual rate of interest as a percentage. This stated rate is based on the assumption interest is paid to your account only once per year. However, in practice interest is usually calculated and added to the account more than once a year. Typically, interest is compounded daily or monthly. This is good news for you because the compounded rate, which is referred to as the effective interest rate, is always slightly higher than the stated interest rate.

#### Step 1

Convert the stated interest rate to decimal form by dividing by 100. Thus, a 4 percent rate equals 0.04.

#### Step 2

Divide the stated interest rate by the number of times interest is calculated and added to the account each year. For example, if interest is compounded daily, divide by 365. This is sometimes called the periodic interest rate.

#### Step 3

Add the periodic interest rate to 1. Raise the result to the power equal to the number of times interest is compounded annually. “Raise to the power of” means to multiply a number by itself a specified number of times, called the power or exponent. For example, if interest is calculated monthly, use an exponent of 12. Suppose your periodic interest rate is 0.004. Add 1 to get 1.004. We'll call this the compounding factor. Write the compounding factor down (or enter it in a calculator). Next, write (or enter) it down again and multiply the two figures together. This raises the compounding factor to the second power. Multiply the result by the compounding factor (or 1.004) again to raise it to the third power. Repeat until you reach the desired power, or exponent, which is 12 in this example.

#### Step 4

Subtract 1 from the result in Step 3. The answer is the effective rate of interest in decimal form. To convert to a percentage, multiply by 100.

#### Tips

- If your calculator has an exponent function, you can simplify the calculation by entering the exponent and pressing the exponent key. Calculators have exponent keys in different locations, so consult the manufacturer's instructions if you can't find it.
- The concept of effective interest rate is often applied to other financial situations involving interest. For example, suppose you have a mortgage with a 6 percent interest rate. Interest is normally calculated and added to the balance you owe on a monthly basis. The effect of this is that your effective interest rate is slightly more than the stated annual percentage rate.

#### References

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