Annual percentage yield (APY) is the effective annual rate, or real rate, of return of an investment if the interest earned each period is compounded. APY considers the effects of compounding, since advertised rates are typically the rates of return for simple interest. The formula for APY is as follows:
- r = Annual interest rate
- n = Number of compounding periods per year
When a balance earns compounded interest, the balance at the end of the total time period is greater than what the balance would be if the balance were to earn simple interest. APY shows you your true rate of return to account for this compounding effect. Let’s look at an example.
Suppose you invest $1,000 in an account that pays 5.0% interest compounded monthly. If you were to earn simple interest, you would end the first year with an account balance of $1,050. Here, since we earn compound interest, you would end the first year with an account balance of $1,051.16. Now, your real rate of return must be greater than 5.0%, so what is it?
We must first define our variables in the equation. Here, r is 0.05. The number of compounding periods, n, is 12, since interest is compounded monthly. Now, all we have to do is plug our variables into the equation and solve. The work is shown below:
So, your annual percentage yield is 5.1162%, which is the effective annual yield on your investment. It’s not much higher than 5.0%, but over time or with a larger initial account balance, this small amount ends up making a big difference!