Answer:
Option A- $1106.18.
Step-by-step explanation:
Given : Don is buying a home for $190,300. He is making a 30% down payment and financing the rest with a 15-year loan at 5.75% interest.
To find : What will his monthly mortgage payment be?
Solution :
There is a 30% down payment
So, Amount financing [tex]=190300-190300\times 30\%[/tex]
[tex]= 190300-190300\times0.3[/tex]
[tex]= 190300-57090=133210[/tex]
Formula of monthly payment :
Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
Discount factor [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
Where, Amount = $133210
Rate r= 5.75%=0.0575
[tex]i=\frac{0.0575}{12}=0.00479[/tex]
Time = 15 years
[tex]n=15\times12=180[/tex]
Now, put all the values we get,
[tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
[tex]D=\frac{1-(1+0.00479)^{-180}}{0.00479}[/tex]
[tex]D=\frac{1-(1.00479)^{-180}}{0.00479}[/tex]
[tex]D=\frac{1-0.423}{0.00479}[/tex]
[tex]D=\frac{0.577}{0.00479}[/tex]
[tex]D=120.459[/tex]
Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
[tex]M=\frac{133210}{120.459}[/tex]
[tex]M=1106.18[/tex]
Therefore, Option A is correct.
The Monthly payment is $1106.18.
