Question

How much would Carol have to invest today at 4.8% compounded annually to have $4400 for a vacation to China in two years?

Answer 1

`\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\to &\$4400\\ P=\textit{original amount deposited}\\ r=rate\to 4.8\%\to (4.8)/(100)\to &0.048\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &2 \end{cases} \\\\\\ 4400=P\left(1+(0.048)/(1)\right)^(1\cdot 2)\implies \cfrac{4000}{\left( 1+0.048 \right)^2}=P`