Question

Determine the balance in an account that compounds continuously with a rate of 12% after 5 years with an initial investment of $3,500.

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3500\\ r=rate\to 12\%\to (12)/(100)\dotfill &0.12\\ t=years\dotfill &5 \end{cases} \\\\\\ A = 3500e^(0.12\cdot 5) \implies A=3500e^(0.6)\implies A \approx 6377.42`