Question

Suppose Frank places $8500 in an account that pays 14% Interest compounded each year.

Assume that no withdrawals are made from the account.

find the amount after year 1 and year 2

Answer 1

`~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$8500\\ r=rate\to 14\%\to (14)/(100)\dotfill &0.14\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &1 \end{cases}`

`A=8500\left(1+(0.14)/(1)\right)^(1\cdot 1)\implies A=8500(1.14)\implies \boxed{A=9690} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~~~~~~ \textit{Compound Interest Earned Amount}`

`A=P\left(1+(r)/(n)\right)^(nt) \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$8500\\ r=rate\to 14\%\to (14)/(100)\dotfill &0.14\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{each year, thus once} \end{array}\dotfill &1\\ t=years\dotfill &2 \end{cases} \\\\\\ A=8500\left(1+(0.14)/(1)\right)^(1\cdot 2)\implies A=8500(1.14)^2\implies \boxed{A=11046.6}`