Question

$1000 is invested at 8%/a compounded daily for 10 years. What is the total interest earned?

Please help

Answer 1

`\bf ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^(rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$1000\\ r=rate\to 8\%\to (8)/(100)\dotfill &0.08\\ t=years\dotfill &10 \end{cases} \\\\\\ A=1000e^(0.08\cdot 10)\implies A=1000e^(0.8)\implies A=2225.54~\hfill \stackrel{interest = A - P}{1225.54}`

btw, we could have used the compound formula just the same, by simply using a compounding cycle of 365, namely daily, assuming a year has 365 days.