Question

Find the amount in a continuously compounded account for the following condition.

​Principal, ​$3000​; Annual interest​ rate, 5.4​%; ​time, 5 years

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& \$3000\\ r=rate\to 5.4\%\to (5.4)/(100)\to &0.054\\ t=years\to &5 \end{cases} \\\\\\ A=3000e^(0.054\cdot 5)\implies A=3000e^(0.27)\implies A\approx 3929.89`