keeping in mind that 6 months is not even a year, since there are 12 months in a year, then 6 months is 6/12, or 1/2 a year, thus
[tex]\bf ~~~~~~ \textit{Simple Interest Earned}
\\\\
I = Prt\qquad
\begin{cases}
I=\textit{interest earned}\to &\$463\\
P=\textit{original amount deposited}\to& \$6000\\
r=rate\to r\%\to \frac{r}{100}\\
t=years\to &\frac{1}{2}
\end{cases}
\\\\\\
463=(6000)(r)\left( \frac{1}{2} \right)\implies \cfrac{463}{(6000)\left( \frac{1}{2} \right)}=r\implies 0.154\approx r
\\\\\\
r\%\approx 100\cdot 0.154\implies r\approx \stackrel{\%}{15.4}[/tex]
