Question

If an investment of $3000 grows to $4432.37 in eight years with interest compounded annually , what is the interest rate?

Answer 1

$\bf \qquad \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\to &\ 4432.37\\ P=\textit{original amount deposited}\to &\ 3000\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &8 \end{cases}$

$\bf 4432.37=3000\left(1+\frac{r}{1}\right)^{1\cdot 8}\implies \cfrac{4432.37}{3000}=(1+r)^8 \\\\\\ \sqrt[8]{\cfrac{4432.37}{3000}}=1+r\implies \sqrt[8]{\cfrac{4432.37}{3000}}-1=r \\\\\\ 0.0500001086\approx r\qquad\qquad\cfrac{r\%}{100}\approx 0.0500001086 \\\\\\ r\%\approx 100\cdot 0.0500001086\implies r=\stackrel{\%}{5}$