[tex]\bf \qquad \qquad \textit{Amortized Loan Value}
\\\\
pymt=P\left[ \cfrac{\frac{r}{n}}{1-\left( 1+ \frac{r}{n}\right)^{-nt}} \right][/tex]
[tex]\bf \begin{cases}
P=
\begin{array}{llll}
\textit{original amount}\\
\end{array}\to &
\begin{array}{rllll}
240,000\\
-downpayment\\
-48,000\\
-----\\
192,000
\end{array}\\
pymt=\textit{periodic payments}\\
r=rate\to 5\frac{3}{4}\%\to \frac{5\frac{3}{4}}{100}\to &0.0575\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{payments are monthly, thus}
\end{array}\to &12\\
t=years\to &30
\end{cases}[/tex]
[tex]\bf pymt=192000\left[ \cfrac{\frac{0.0575}{12}}{1-\left( 1+ \frac{0.0575}{12}\right)^{-12\cdot 30}} \right][/tex]
