[tex]\bf \qquad \qquad \textit{Amortized Loan Value}
\\\\
pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right]
\\\\\\
\qquad
\begin{cases}
P=
\begin{array}{llll}
\textit{original amount}\\
\end{array}\to &
\begin{array}{llll}
200000
\end{array}\\
pymt=\textit{periodic payments}\\
r=rate\to 5\%\to \frac{5}{100}\to &0.05\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{quarterly, thus 4 times}
\end{array}\to &4\\
t=years\to &9
\end{cases}[/tex]
