Question

Jill invested $20,000 in an account that earned 5.5% annual interest, compounded annually. What is the value of this account after 10 years?
Round to the nearest cent.

Answer 1

$\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\ 20000\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}$

$\bf A=20000\left(1+\frac{0.055}{1}\right)^{1\cdot 10}\implies A=20000(1.055)^{10} \\\\\\ A\approx 34162.88916707\implies A\approx \stackrel{\textit{rounded up}}{34162.89}$