Question

Suppose you invest $550 at an annual interest rate of 3% compounded continuously. How much will you have in the account after six years? Round your answer to the nearest cent.

Answer 1

$~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \ 550\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &6 \end{cases} \\\\\\ A=550e^{0.03\cdot 6}\implies A=550e^{0.18}\implies A\approx 658.47$