Question

11000 is compounded semiannually at a rate of 12% for 21 years. Find the total amount in the compound interest account

Answer 1

`\bf ~~~~~~ \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 &\$11000\\ r=rate\to 12\%\to (12)/(100)\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &21 \end{cases}`

`\bf A=11000\left(1+(0.12)/(2)\right)^(2\cdot 21)\implies A=11000(1.06)^(42)\implies A\approx 127127.359416`