Answer:
$1,486.41
Step-by-step explanation:
Purchase price for a house is $309,900 and you put 20% down for a 30 year loan with a fixed rate of 6%.
The amount made by down payment is,
[tex]=309,900\times \dfrac{20}{100}=\$61,980[/tex]
The amount left for monthly payment is,
[tex]=309,900-61,980=\$247,920[/tex]
We know that,
[tex]\text{PV of annuity}=P\left[\dfrac{1-(1+r)^{-n}}{r}\right][/tex]
Here,
PV = Present Value = $247,920,
P = Monthly payment,
r = Monthly rate of interest = [tex]\dfrac{0.06}{12}[/tex]
n = number of months = 30 years = 360 months
Putting the values,
[tex]\Rightarrow 247920=P\left[\dfrac{1-(1+\frac{0.06}{12})^{-360}}{\frac{0.06}{12}}\right][/tex]
[tex]\Rightarrow P=\dfrac{247920}{\left[\dfrac{1-(1+\frac{0.06}{12})^{-360}}{\frac{0.06}{12}}\right]}[/tex]
[tex]\Rightarrow P=\$1,486.41[/tex]
