Question

​$10000 is compounded semiannually at a rate of 10​% for 20 years.

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 10000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{semiannually, thus twice} \end{array}\dotfill &2\\ t=years\dotfill &20 \end{cases}$

$\bf A=10000\left(1+\frac{0.10}{2}\right)^{2\cdot 20}\implies A=10000(1.05)^{40}\implies A\approx 70399.88712125$