The annual percentage yield provides a means for estimating the return on an investment with compound interest in terms of its effective annual yield.

To find the APY, one uses the following formula:

$$

\mathrm{APY}=\frac{1}{t}\left(\left( 1+\frac{r}{n} \right)^{nt}-1\right)

where $n$ is the number of compounding periods per year, $t$ is the number of years and $r$ is the rate.

For example, an investment compounded quarterly at 3% interest for 2 years will have an APY of:

$$

\mathrm{APY}=\frac{1}{2}\left(\left( 1+\frac{.03}{4} \right)^{(4)(2)}-1\right) \approx.0308 or an APY of 3.08%

$100 invested under the above terms would generate $3.08 in interest the first year. If the interest is deposited and continues to grow with the principal, then the account would earn $3.17 in the second year because $0.08 interest would be earned on first year's interest.

External links

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• APY on Investopedia

Mathematical finance