Explanation
to find the regular monthly payment amount we need to use the formula:
[tex]A=P\frac{r(1+r)^{n}}{(1+r)^{n}-1}[/tex]so
Step 1
find the principal,
if you make a 20% down , it means the rest is 80 %, so the Principal will be 80 % of the total
[tex]\begin{gathered} Principal=\text{ whole cost*80 \%} \\ P=230000*\frac{80}{100} \\ P=184000 \end{gathered}[/tex]Step 2
now, find the regular monthly payments amount
a) let
[tex]\begin{gathered} Principal\text{ = P=184000} \\ time=15\text{ years =}15\text{ years*}\frac{12\text{ months}}{1\text{ year}}=180\text{ months} \\ r=5\text{ \% = }\frac{5}{100}=0.05 \end{gathered}[/tex]b) replace
[tex]\begin{gathered} A=P\frac{r(1+r)^n}{(1+r)^n-1} \\ A=184000\frac{0.05(1+0.05)^{180}}{(1+0.05)^{180}-1} \\ A=9201.41 \end{gathered}[/tex]so, the answer is 9201.41
