Question

$500 is deposited in an account with 7% interest rate, compounded continuously. What is the balance after 10 years? Round to the nearest cent.

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 7\%\to (7)/(100)\dotfill &0.07\\ t=years\dotfill &10 \end{cases} \\\\\\ A = 500e^(0.07\cdot 10) \implies A \approx 1006.88`