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+(r)/(n)\right)^(n)-1 \\\\ \begin{cases} r=rate\to 5.9\%\to (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+(0.059)/(4)\right)^(4)-1\implies (1.01475)^4-1 \approx 0.0603 \\\\\\ 0.0603\cdot 100\implies \stackrel{\%}{6.03}`