Question

Find how much should be invested to have 19,500 in 10 months at 7.5% simple interest

Answer 1

keeping in mind that 10 months is not even a year, since there are 12 months in a year, then 10 months is just 10/12 of a year, or 5/6.


`\bf \qquad \textit{Simple Interest Earned Amount}\\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\to &\$19500\\ P=\textit{original amount deposited}\\ r=rate\to 7.5\%\to (7.5)/(100)\to &0.075\\ t=years\to (10)/(12)\to &(5)/(6) \end{cases} \\\\\\ 19500=P\left( 1+0.075\cdot (5)/(6) \right)\implies 19500=P(1.0625) \\\\\\ \cfrac{19500}{1.0625}=P\implies 18352.941176470\approx P`