# Stated Interest Rate vs. Effective Interest Rate

There is a difference between stated interest rate and the effective interest rate.
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"No loan or investment is right, unless the price is right" is a colloquialism of novice and experienced investors alike.

For a member of either group to make an informed investment or purchase, the person must understand the true cost or benefit of that financial decision. To recognize a decision's true cost or benefit requires that you understand the difference between a stated interest rate and an effective interest rate.

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## Stated Interest Rate

A stated annual interest rate (SAR,) or simple interest rate, is the interest rate you'll pay on a loan or earn on an investment per year. The SAR is a simple interest that's calculated on the principal of a loan or investment, rather than a compound interest, which is based on both the principal amount and the interest accumulated in prior periods.

Simple interest is an annualized rate that does not account for intra-year compounding of interest. Consequently, the effective rate will be the same as the stated interest rate.

## Effective Interest Rate

An effective interest rate incorporates the effect of intra-year compounding that occurs on a quarterly, monthly or daily basis. The more frequently the interest is compounded, the higher the effective interest rate.

For a loan that compounds interest, and does so frequently, the effective interest rate will be significantly higher than the stated interest rate. You use the effective annual interest rate to determine the actual return on investment as well as the true interest rate on a loan.

## Stated Interest vs. Effective Interest

When an investment earns compound interest, the stated and actual interest rates are equal only when interest is compounded annually.

The stated interest rate does not account for the effect of compound interest on the amount you'll owe a creditor or that you'll receive in the form of interest on an investment. In this way, stated interest is unlike the effective interest rate that accounts for compound interest.

Consequently, because a bank loan quote will be documented using a stated interest rate, rather than an effective annual interest rate, you may assume you'll owe that lower rate. But in reality, rather than pay, for example, the principal and 20 percent interest that's stated on a loan document, you'll owe the principal and effective annual interest of 23.94 percent.

In contrast, a financial institution may tout the effective annual rate in its advertising, rather than an investment's stated interest rate. For instance, a bank may promote the effective interest rate of 9.43 percent for a deposit, rather than a stated rate of 9 percent.

## Effective Interest Example

Assume that you contracted for a one-year, \$20,000 certificate of deposit (CD) with a stated annual interest rate of 5 percent, compounded monthly, that will earn \$1,000 at maturity.

To calculate what this CD will actually earn each month, or the effective interest rate on the CD, divide 5 percent by 12, or 5/12, to find the investment's effective monthly interest rate of 4.166 percent.

Due to the investment's effective interest rate, at the end of the first month, your savings will grow to \$20,083, or the \$20,000 principal plus \$83 interest, or \$20,000 multiplied by 4.166 percent, which equals \$83.

In month two, you would receive an additional \$83 plus the compound interest on the \$83 you received in the prior month, which is \$3.46. At this point, your savings grows to \$20,169.46. In this way, the interest on your \$20,000 investment compounds each month for the 12-month investment period.