[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount}
\\\\
A=P\left(1+\frac{r}{n}\right)^{nt}
\quad
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{original amount deposited}\to &\$150,000\\
r=rate\to r\%\to \frac{r}{100}\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{semiannually, thus twice}
\end{array}\to &2\\
t=years
\end{cases}[/tex]
[tex]\bf A=150000\left(1+\frac{r}{2}\right)^{2\cdot t}\implies A=150000\left(1+\frac{r}{2}\right)^{2 t}
\\\\\\
\boxed{150000\left(1+\frac{r}{2}\right)^{2 t}~~~~=~~~~150000(1.012)^{2t}}
\\\\\\
\left(1+\frac{r}{2}\right)=(1.012)\implies 1+\cfrac{r}{2}=1.012\implies \cfrac{r}{2}=0.012
\\\\\\
r=0.024\implies r\%=0.024\cdot 100\implies r=\stackrel{\%}{2.4}[/tex]
