Question

If the purchase price for a house is $309,900, what is the monthly payment if you put 20% down for a 30 year loan with a fixed rate of 6%?

Answer 1

If the 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 monthly payment is $1486.41.

Answer 2

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,

$=309,900\times \dfrac{20}{100}=\ 61,980$

The amount left for monthly payment is,

$=309,900-61,980=\ 247,920$

We know that,

$\text{PV of annuity}=P\left[\dfrac{1-(1+r)^{-n}}{r}\right]$

Here,

PV = Present Value = $247,920,

P = Monthly payment,

r = Monthly rate of interest = $\dfrac{0.06}{12}$

n = number of months = 30 years = 360 months

Putting the values,

$\Rightarrow 247920=P\left[\dfrac{1-(1+\frac{0.06}{12})^{-360}}{\frac{0.06}{12}}\right]$

$\Rightarrow P=\dfrac{247920}{\left[\dfrac{1-(1+\frac{0.06}{12})^{-360}}{\frac{0.06}{12}}\right]}$

$\Rightarrow P=\ 1,486.41$