Question

an initial amount of $3100 is invested in an account at an interest rate of 4.5% per year, compounded continuously. assuming that no withdrawals are made, fine the amount in the account after five years

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3100\\ r=rate\to 4.5\%\to (4.5)/(100)\dotfill &0.045\\ t=years\dotfill &5 \end{cases} \\\\\\ A=3100e^(0.045\cdot 5) \implies A=3100e^(0.225)\implies A \approx 3882.2`