Respuesta :
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.
[tex]\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 \frac{r}{100}\\ t=years\to \frac{6}{12}\to &\frac{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[/tex]
[tex]\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 \frac{r}{100}\\ t=years\to \frac{6}{12}\to &\frac{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[/tex]
