Question

Janet deposited $9,600 into an account that pays 4.4 interest, compounded daily. At the end of nine months, how much interest has she earned

Answer 1

bearing in mind that 9 months is not even a year, but since there are 12 months in a year, then 9 months is really 9/12 years.

$\bf ~~~~~~ \stackrel{\textit{daily}}{\textit{Continuously}} \textit{Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \ 9600\\ r=rate\to 4.4\%\to \frac{4.4}{100}\dotfill &0.044\\ t=years\to \frac{9}{12}\dotfill &\frac{3}{4} \end{cases} \\\\\\ A=9600e^{0.044\cdot \frac{3}{4}}\implies A=9600e^{0.033}\implies A\approx 9922.09$

$\bf \stackrel{\textit{interest earned}}{9922.09-9600\implies 322.09}$