Question

you put 500$ in a savings account. The account earns 15.75$ simple interest in 6 months.what is the annual interest rate

Answer 1

$76.50 because there is 12 months and half of that is $75.59

Answer 2

keeping in mind that 6 months is not even a year, since there are 12 months in a year, then 6 months is really 6/12 years, or 1/2 year.


`\bf \qquad \textit{Simple Interest Earned}\\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\to &\$15.75\\ P=\textit{original amount deposited}\to& \$500\\ r=rate\to r\%\to (r)/(100)\\ t=years\to (6)/(12)\to &(1)/(2) \end{cases} \\\\\\ 15.75=500\cdot r\cdot \cfrac{1}{2}\implies \cfrac{15.75}{500}=\cfrac{r}{2}\implies \cfrac{2\cdot 15.75}{500}=r \\\\\\ 0.063=r\implies 0.063=\cfrac{r}{100}\implies 0.063\cdot 100=r\implies 6.3\%=r`