[tex]\bf \qquad \textit{Compound Interest Earned Amount}\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\\ \quad \\
\begin{cases}
A=\textit{current amount}\to &6,000\\
P=\textit{original amount deposited}\to &\$2,500\\
r=rate\to r\%\to \frac{r}{100}\to &0.0r\\
n=\textit{times it compounds per year, quarterly}\to &4\\
t=years\to &10
\end{cases}
\\ \quad \\
meaning
\\ \quad \\
6,000=2,500\left(1+\frac{r}{4}\right)^{4\cdot 10}[/tex]
solve for "r"
notice, the "r" value, goes in the equation as a decimal, so 5% is really 5/100 or 0.05 25% is 0.25 and so on
so... the "r" that you'll get, will be a decimal value, multiply that by 100, and you'll get the percentage notation of it
[tex]\bf 6,000=2,500\left(1+\frac{r}{4}\right)^{4\cdot 10}\implies\cfrac{6000}{2500}=\left(1+\frac{r}{4}\right)^{40}
\\ \quad \\
\cfrac{12}{5}=\left(1+\frac{r}{4}\right)^{40}\impliedby \textit{now, taking root }\sqrt[40]{\qquad }
\\ \quad \\
\sqrt[40]{\cfrac{12}{5}}=\sqrt[40]{\left(1+\frac{r}{4}\right)^{40}}\implies \sqrt[40]{\cfrac{12}{5}}=1+\cfrac{r}{4}
\\ \quad \\
\sqrt[40]{\cfrac{12}{5}}-1=\cfrac{r}{4}\implies 4\left( \sqrt[40]{\cfrac{12}{5}}-1 \right)=r \\ \quad \\
[/tex]
[tex]\bf 0.0885119586095070592=r\implies 0.0885\cdot 100\implies 8.85\%=r[/tex]
