Question

Find the amount of time to the nearest day it would take a deposit of $1300 to grow to 1 million at 17% compounded continuously. The amount of time it would take to grow the deposit to $1 million is____ years ___ days

Answer 1

$\bf \qquad \textit{Simple Interest Earned}\\\\ A = Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\to 1000000\\ P=\textit{original amount deposited}\to& \ 1300\\ r=rate\to 17\%\to \frac{17}{100}\to &0.017\\ t=years \end{cases}$

$\bf 1000000=1300e^{0.17t}\implies \cfrac{1000000}{1300}=e^{0.17t}\implies \cfrac{10000}{13}=e^{0.17t} \\\\\\ ln\left( \frac{1000000}{1300} \right)=ln(e^{0.17t})\implies ln\left( \frac{1000000}{1300} \right)=0.17t \\\\\\ \cfrac{ln\left( \frac{1000000}{1300} \right)}{0.17}=t\impliedby years$

now, how many days? simply multiply t * 365.