Respuesta :
Answer:
Monthly payment is $1448.82
Step-by-step explanation:
Given : Abbey purchased a house using a fixed rate mortgage. The annual interest rate is 4.2% compounded monthly for 20 years. The mortgage amount is $235,000.
To find : What is the monthly payment on the mortgage?
Solution : First we find the monthly payment
Formula of monthly payment Â
Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex] Â
Discount factor [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex] Â
Where, Amount = $235,000
Rate r= 4.2%=0.042 Â
[tex]i=\frac{0.042}{12}=0.0035[/tex] Â
Time = 20 years Â
[tex]n=20\times12=240[/tex] Â
Now, put all the values we get, Â
[tex]D=\frac{1-(1+i)^{-n}}{i}[/tex] Â
[tex]D=\frac{1-(1+0.0035)^{-240}}{0.0035}[/tex] Â
[tex]D=\frac{1-(1.0035)^{-240}}{0.0035}[/tex] Â
[tex]D=\frac{1-0.4323}{0.0035}[/tex] Â
[tex]D=\frac{0.5677}{0.0035}[/tex] Â
[tex]D=162.2[/tex] Â
Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex] Â
[tex]M=\frac{235000}{162.2}[/tex] Â
[tex]M=1448.82[/tex] Â
Approximately,monthly payment is $1448.82
