Answer
$r_e = (1+\frac{r}{n})^{n}-1$, where $r_e$ is the effective annual yield.
Work Step by Step
This is the formula we use when we make calculations with compound interest:
$A = P~(1+\frac{r}{n})^{nt}$
$A$ is the final amount in the account
$P$ is the principal (the amount of money invested)
$r$ is the interest rate
$n$ is the number of times per year the interest is compounded
$t$ is the number of years
This is the formula we use when we make calculations with simple interest:
$A = P~(1+r_et)$, where we can let $r_e$ be the effective annual yield.
To derive the equation for effective annual yield $r_e$, we can equate the two equations.
$P~(1+r_et) = P~(1+\frac{r}{n})^{nt}$
Note that the time period is one year, so $t = 1$.
$P~(1+r_et) = P~(1+\frac{r}{n})^{nt}$
$P~(1+r_e) = P~(1+\frac{r}{n})^{n}$
$(1+r_e) = (1+\frac{r}{n})^{n}$
$r_e = (1+\frac{r}{n})^{n}-1$
This is the equation for the effective annual yield.
