Question

How much money should you invest in a savings account that pays 2.25% interest compounded quarterly to have a balance of $1,196.61 after 8 years

Answer 1

`\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\dotfill&1196.61\\ P=\textit{original amount deposited}\\ r=rate\to 2.25\%\to (2.25)/(100)\dotfill &0.0225\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &8 \end{cases}`

`\bf 1196.61=P\left(1+(0.0225)/(4)\right)^(4\cdot 8)\implies 1196.61=P(1.005625)^(32) \\\\\\ \cfrac{1196.61}{(1.005625)^(32)}=P\implies 999.9969 \approx P`