Question

On the day of a child's birth, a parent deposits $25,000 in a trust fund that pays 3% interest, compounded continuously. determine the balance in this account on the child's 26th birthday. (round your answer to two decimal places.)

Answer 1

well, on the child's 26th birthday that'll be 26 years later, so

$~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \ 25000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &26 \end{cases} \\\\\\ A=25000e^{0.03\cdot 26}\implies A=25000e^{0.78}\implies A\approx 54536.81$