Question

How much would $150 invested at 8% interest compounded continuously be worth after 17 years? Round your answer to the nearest cent. A(t) = P•e^rt

A. $555.00
B. $584.43
C. $354.00
D. $471.39
​

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$150\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ t=years\dotfill &17 \end{cases} \\\\\\ A = 150e^(0.08\cdot 17)\implies A=150e^(1.36) \implies A \approx 584.43`