Question

Use the continuous compound interest formula to find the indicated value. A=90,000; P=65,452; r=9.1%; t=? t=years (Do not round until the final answer. Then round to two decimal places as​ needed.)

Answer 1

$\bf \qquad \textit{Simple Interest Earned}\\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\to &90,000\\ P=\textit{original amount}\to& \ 65,452\\ r=rate\to 9.1\%\to \frac{9.1}{100}\to &0.091\\ t=years \end{cases}$

$\bf 90000=65452e^{0.091t}\implies \cfrac{90000}{65452}=e^{0.091t}\implies \cfrac{22500}{16363}=e^{0.091t} \\\\\\ \textit{taking \underline{ln} to both sides}\qquad ln\left( \cfrac{22500}{16363} \right)=ln\left( e^{0.091t} \right) \\\\\\ ln\left( \cfrac{22500}{16363} \right)=0.091t\implies \cfrac{ln\left( \frac{22500}{16363} \right)}{0.091}=t$