[tex]\bf ~~~~~~~~~~~~ \textit{Amortized Loan Value}
\\\\
pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right]
\\\\\\
~~~~~~
\begin{cases}
P=
\begin{array}{llll}
\textit{original amount deposited}\\
\end{array}\to &\$146800\\
pymt=\textit{periodic payments}\\
r=rate\to 5.25\%\to \frac{5.25}{100}\to &0.0525\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{monthly, thus twelve}
\end{array}\to &12\\
t=years\to &30
\end{cases}[/tex]
[tex]\bf pymt=146800\left[ \cfrac{\frac{0.0525}{12}}{1-\left( 1+ \frac{0.0525}{12}\right)^{-12\cdot 30}} \right]
\\\\\\
pymt=146800\left[ \cfrac{0.004375}{1-\left(1.004375\right)^{-360}} \right]
\\\\\\
pymt\approx 146800\left[ \cfrac{0.004375}{0.7968815551191}\right]\implies pymt\approx 805.9541545[/tex]
