## Thinking Mathematically (6th Edition)

$r_e = (1+\frac{r}{n})^{n}-1$, where $r_e$ is the effective annual yield.
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.