Answer:
Option 4 - $699.03
Step-by-step explanation:
Given : If Gerry is approved for a $150,000 mortgage at 3.75 percent interest for a 30-year loan
To find : What would the monthly payment be?
Solution :
Formula of monthly payment
[tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
Discount factor [tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
Where, Amount = $150,000
Rate r= 3.75%=0.0375
[tex]i=\frac{0.0375}{12}=0.003125[/tex]
Time = 30 years
[tex]n=30\times 12=360[/tex]
Now, put all the values we get,
[tex]D=\frac{1-(1+i)^{-n}}{i}[/tex]
[tex]D=\frac{1-(1+0.003125)^{-360}}{0.003125}[/tex]
[tex]D=\frac{1-(1.003125)^{-360}}{0.003125}[/tex]
[tex]D=\frac{1-0.3252}{0.003125}[/tex]
[tex]D=\frac{0.6747}{0.003125}[/tex]
[tex]D=215.928[/tex]
Monthly payment, [tex]M=\frac{\text{Amount}}{\text{Discount factor}}[/tex]
[tex]M=\frac{150000}{215.928}[/tex]
[tex]M=694.673[/tex]
Approximately, The monthly payment is $699.03
Therefore, Option 4 is correct.
