Question

Suppose you invest $400 at an annual interest rate 7.6% compounded continuously. How much will you have in the account after 1.5 years? Round the solution to the nearest dollar

Answer 1

$\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount}\\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to& \ 400\\ r=rate\to 7.6\%\to \frac{7.6}{100}\to &0.076\\ t=years\to &1.5 \end{cases} \\\\\\ A=400e^{0.076\cdot 1.5}\implies A=400e^{0.114}$