Question

An investment declines in value by 3% each month. By what percentage does its value decline in a year ?

Answer 1

$\bf \qquad \qquad \textit{Annual Yield Formula} \\\\ ~~~~~~~~~~~~\left(1+\frac{r}{n}\right)^{n}-1 \\\\ \begin{cases} r=rate\to 3\%\to \frac{3}{100}\to &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\to &12 \end{cases} \\\\\\ \left(1+\frac{0.03}{12}\right)^{12}-1\implies 1.0025^{12}-1~~\approx ~~ 0.03041596 \\\\\\ r\%=0.03041596\cdot 100\implies r\approx\stackrel{\%}{3.04}$