The Interest Rate vs. the Annual Percentage Yield

The fundamental difference between the interest rate and the APY is that the interest rate is a tool and the APY is the result of the use of that tool. The institution uses the interest rate to calculate the amount of interest the account earns over a given period of time. The APY, on the other hand, reflects the result of the interest calculations and the compounding frequency. It is the yield, expressed as a percentage of the account balance, that the interest rate and compounding produce over a year.

For example, suppose an institution will pay interest at the annual rate of 3 percent, compounded every six months. Assume an initial deposit of $1,000.

After six months, the institution applies 1.5 percent (i.e., one-half of the annual 3 percent rate) to the $1,000 balance and determines that the account has earned $15 over the first six months.

Since compounding is every six months, the $15 is added to the principal and earns interest itself. So for the next six months, the principal balance is $1,015.

At the end of the next six months, the institution calculates the interest by applying 1.5 percent to $1,015, which yields $15.225. Suppose the institution rounds this amount up to $15.23.

So the total interest yield for the year is $30.23 ($15 plus $15.23). For an account with no stated maturity, the formula for the APY is 100 (interest/principal), or 100 (30.23/1000) or 3.23 percent. You can see that the compounding has caused the APY to be greater than the interest rate, which is 3 percent.

As this example shows, there will be a difference between the APY and the interest rate on any account for which the institution compounds interest more frequently than once per year.

Another circumstance where there will be a difference between the APY and the interest rate: If the account has a stated maturity of greater than one year and does not compound interest on an annual or more frequent basis and requires the consumer to withdraw interest at least annually, the APY formula can actually produce a rate that is less than the annual interest rate. In such a case, the institution can disclose an APY that is equal to the interest rate. {12 CFR 1030, Appendix A, Part I, Para. E]