Question

Alexis put $2000 in a savings account. After 4 years, she had $2543 in the

account. What rate of interest did she earn? Use the formula A = Pert, where A

Answer 1

Alexis would have earned $543 in interest

Answer 2

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2543\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to r\%\to (r)/(100)\\ t=years\dotfill &4 \end{cases}`

`2543=2000e^{(r)/(100)\cdot 4}\implies \cfrac{2543}{2000}=e^{(r)/(25)}\implies \log_e\left( \cfrac{2543}{2000}\right)=\log_e\left( e^{(r)/(25)} \right) \\\\\\ \ln\left( \cfrac{2543}{2000}\right)=\cfrac{r}{25}\implies 25\ln\left( \cfrac{2543}{2000}\right)=r\implies 6\approx r`