Answer:
Option 2 -$852
Step-by-step explanation:
Given : You have decided to buy a new home and the bank offers you a 30 year fixed loan at 5.5% on a balance of $150,000.
To find : The monthly payment?
Solution :
Formula of monthly payment,
[tex]\text{Monthly payment}=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
Discount factor [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
Put the value,
[tex]M=\frac{A\times i}{1-(1+i)^{-n}}[/tex]
Where, A=$150000
r=5.5%=0.055
[tex]i=\frac{0.055}{12}=0.004583[/tex]
t=30 year
[tex]n=30\times 12=360[/tex]
Substitute all the values,
[tex]M=\frac{150000\times 0.004583}{1-(1+0.004583)^{-360}}[/tex]
[tex]M=\frac{150000\times 0.004583}{1-(1.004583)^{-360}}[/tex]
[tex]M=\frac{687.5}{1-0.19277}[/tex]
[tex]M=\frac{687.5}{0.80722}[/tex]
[tex]M=\$851.68[/tex]
Approximately, Monthly payment is $852.
Therefore,Option 2 is correct.
