Question

A person places $81200 in an investment account earning an annual rate of 3. 6%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 13 years

Answer 1

`~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$81200\\ r=rate\to 3.6\%\to (3.6)/(100)\dotfill &0.036\\ t=years\dotfill &13 \end{cases} \\\\\\ A=81200e^(0.036\cdot 13)\implies A=81200e^(0.468)\implies A\approx 129659.95`