Chapter R.1, Problem 46E

Annual yield. The annual interest rate $r$, when compounded more than once a year, results in a slightly higher yearly interest rate; this is called the annual (or effective) yield and denoted as Y. For example, $1000 deposited at $5\%$, compounded monthly for 1 yr (12 months), will have a value given by $A=1000{\left(1+\frac{0.05}{12}\right)}^{12}=\$1051.16$.

The interest earned is $\$51.16/\$1000$, or 0.05116, which is $5.116\%$ of the original deposit. Thus, we say that this account has a yield of $\text{Y}=0.05116$, or $5.116\%$.

The formula for annual yield depends on the annual interest rate $r$ and the compounding frequency $n$ :

$Y={\left(1+\frac{r}{n}\right)}^n-1$

For Exercises 43-46, find the annual yield as a percentage, to two decimal places, given the annual interest rate and the compounding frequency.

46. Annual interest rate of $4\%$, compounded daily