Chapter 8.2, Problem 19E

Savings institutions often state a nominal rate, which you can think of as a simple annual interest rate, and the effective interest rate, which is the actual interest rate earned due to compounding. Given the nominal rate, it is easy to calculate the effective interest rate as follows. Assume that you invest $1 in an account paying an interest rate of 6% compound monthly. Using the compound interest formula

$\text{A=P}{\left(\text{1+}\frac{\text{r}}{\text{m}}\right)}^{\text{n}}$, with P = 1, r = 0.06, m = 12, and n = 12, we would get

$\text{A=}{\left(\text{1+}\frac{\text{0}\text{.06}}{\text{12}}\right)}^{12}\approx 1.0617$. So the effective interest rate is

1.0617 – 1 = 0.0617, or 6.17%. Use this method to find the effective interest rate for the investments in Exercises $19-22$.

nominal yield, 7.5%; compounded monthly