Question

Sara invested $8,000 at 6% compounded daily. Five years later she withdrew the full amount to use as a down payment on a house. How much money did she have for the down payment? Assume there are 365 days in a year.

Answer 1

$\bf ~~~~~~ \stackrel{\textit{Daily Compounding}}{\textit{Continuously Compounding}} \textit{ Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \ 8000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ t=years\dotfill &5 \end{cases} \\\\\\ A=8000e^{0.06\cdot 5}\implies A=8000e^{0.3}\implies A\approx 10798.87$