Question

You are looking to invest $20,000. A bank

offers to give you 6% on all deposits,
compounded continuously. If you were to
invest your money with them, how much
would you expect to have in your account
after 25 years?
Round your answer to the nearest cent (hundredth)

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 6\%\to (6)/(100)\dotfill &0.06\\ t=years\dotfill &25 \end{cases} \\\\\\ A = 20000e^(0.06\cdot 25) \implies A=20000e^(1.5) \implies A \approx 89633.78`