Question

Four years ago you invested some money at 10% interest. you now have $439.23 in the account. if the interest was compounded yearly, how much did you invest 4 years ago?

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$439.23\\ P=\textit{original amount deposited}\\ r=rate\to 10\%\to (10)/(100)\dotfill &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases}`

`439.23=P\left(1+(0.1)/(1)\right)^(1\cdot 4)\implies 439.23=P(1.1)^4 \\\\\\ \cfrac{439.23}{1.1^4}=P\implies 399.3=P`