Question

How long will it take $15,000 to double if you invest the money in an account earning

4.75% interest compounded continuously? Round to the nearest tenth of a year.

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$15000\\ r=rate\to 4.75\%\to (4.75)/(100)\dotfill &0.0475\\ t=years \end{cases}`

`30000 = 15000e^(0.0475\cdot t) \implies \cfrac{30000}{15000}=e^(0.0475t)\implies 2=e^(0.0475t) \\\\\\ \log_e(2)=\log_e(e^(0.0475t))\implies \log_e(2)=0.0475t \\\\\\ \ln(2)=0.0475t\implies \cfrac{\ln(2)}{0.0475}=t\implies 14.6\approx t`