Question

Dolores invests $8100 in a new savings account which earns 3. 2 % annual interest, compounded continuously. What will be the value of her

investment after 9 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 & \$8100\\ r=rate\to 3.2\%\to (3.2)/(100)\dotfill &0.032\\ t=years\dotfill &9 \end{cases} \\\\\\ A = 8100e^(0.032\cdot 9)\implies A=8100e^(0.288) \implies A \approx 10803.43`