Question

Determine the interest paid in an account that compounds continuously with a rate of 15% after 3 years with an initial investment of $500

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$500\\ r=rate\to 15\%\to (15)/(100)\dotfill &0.15\\ t=years\dotfill &3 \end{cases} \\\\\\ A = 500e^(0.15\cdot 3) \implies A=500e^(0.45)\implies A \approx 784.16\hspace{6em}\underset{ interest }{\stackrel{ 784.16~~ - ~~500 }{\boxed{\approx 284.16}}}`