Chapter 4.6, Problem 35E

(a)

To determine

To prove: The effective rate of interest $r_{eff}$ that will produce the same interest per year as the nominal rate $r$ compounded $n$ times per year is given by the formula:

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

(b)

To determine

To prove: The effective rate of interest $r_{eff}$ that will produce the same interest per year as the nominal rate $r$ compounded continuously is given by the formula:

$r_{eff}=e^r-1$