Question

Determine the effective rate for $1 for 1 year at 5.9% compounded quarterly.

Answer 1

Keeping in mind that the effective rate, is in effect the APY or Annual Percentage Yield, 

$\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ ~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 5.9\%\to \frac{5.9}{100}\to &0.059\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four times} \end{array}\to &4 \end{cases} \\\\\\ \left(1+\frac{0.059}{4}\right)^{4}-1\implies (1.01475)^4-1 \approx 0.0603 \\\\\\ 0.0603\cdot 100\implies \stackrel{\%}{6.03}$