[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 loaned}\\
\textit{there's a downpayment}\\
\textit{of 20\%, or 59,200}\\
\end{array}\to &
\begin{array}{llll}
296,000\\
-59,200\\
\underline{236,800}
\end{array}\\
pymt=\textit{periodic payments}\\
r=rate\to 6\%\to \frac{6}{100}\to &0.06\\
n=
\begin{array}{llll}
\textit{times it compounds per year}\\
\textit{she's making monthly payments}
\end{array}\to &12\\
t=years\to &30
\end{cases}[/tex]
notice, the amount that'd be compounded of the loan, is just the 80%, because she put a downpayment of 20%, so, that doesn't get any interest, thus P = 236,800
