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+(r)/(n)\right)^(n)-1 \\\\ \begin{cases} r=rate\to 3\%\to (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+(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}`