Explanation
We are simply asked to obtain the monthly payment on the house loan
To do this, we will make use of the formula to compute the equal monthly payment (EMI)
[tex]\begin{gathered} The\text{ principal here will be:} \\ (100-20)\text{ \% }\times$ \text{ \$}224,000 $ \end{gathered}[/tex][tex]P=0.8\times224,000=\text{ \$179200}[/tex]Next, we know that there are 12 months in a year
In 30 years, there will be
[tex]30\times12=360\text{ months}[/tex]This means that
[tex]n=360[/tex][tex]\begin{gathered} r=\frac{5.3\text{ \%}}{12} \\ \\ r=\frac{0.053}{12} \\ \\ r=0.00441 \\ \end{gathered}[/tex]We can now substitute the values above to get EMI
[tex]EMI=179200\times\frac{0.00441(1+0.00441)^{360}}{(1+0.00441)^{360}-1}[/tex]Simplifying further
[tex]EMI=\text{ \$994.216}[/tex]Hence, the monthly payment is $994.22
