Question

You deposit $7550 in an account that pays 7.25% interest, compounded continuously. How long to the

Answer 1

$~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \ \stackrel{tripled}{(7550)3}\\ P=\textit{original amount deposited}\dotfill & \ 7550\\ r=rate\to 7.25\%\to \frac{7.25}{100}\dotfill &0.0725\\ t=years \end{cases}$

$3(7550)=7550e^{0.0725\cdot t}\implies \cfrac{3(7550)}{7550}=e^{0.0725t}\implies 3=e^{0.0725t} \\\\\\ \log_e(3)=\log_e\left( e^{0.0725t} \right)\implies \ln(3)=0.0725t \\\\\\ \cfrac{\ln(3)}{0.0725}=t\implies 15.15327\approx t\implies 15\approx t$