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 (4.4)/(100)\dotfill &0.044\\ t=years\to (9)/(12)\dotfill &(3)/(4) \end{cases} \\\\\\ A=9600e^{0.044\cdot (3)/(4)}\implies A=9600e^(0.033)\implies A\approx 9922.09 \\\\\\`

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