Question

Camden is going to invest $600 and leave it in an account for 12 years. Assuming the

Answer 1

$~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \ 920\\ P=\textit{original amount deposited}\dotfill & \ 600\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &12 \end{cases}$

$920=600e^{\frac{r}{100}\cdot 12}\implies \cfrac{920}{600}=e^{\frac{3r}{25}}\implies \cfrac{23}{15}=e^{\frac{3r}{25}}\implies \log_e\left( \cfrac{23}{15} \right)=\log_e\left( e^{\frac{3r}{25}} \right) \\\\\\ \ln\left( \cfrac{23}{15} \right)=\cfrac{3r}{25}\implies 25\cdot \ln\left( \cfrac{23}{15} \right)=3r\implies \cfrac{25\cdot \ln\left( \frac{23}{15} \right)}{3}=r \\\\\\ 3.5620\approx r\implies \stackrel{\%}{3.56}\approx r$