Answer:
$132.93
Step-by-step explanation:
We will use annuity formula, which is:
[tex]P=C[\frac{1-(1+r)^{-n}}{r}][/tex]
Where P is the loan amount
C is the monthly payment
r is the rate of interest [monthly]
n is the time period [in months]
Firstly, let's calculate her normal monthly payment (without purchasing points):
P is 105,000
C is what we need to find
r is the 0.045/12 = 0.00375
n is 12*30 = 360
Now, we have:
[tex]P=C[\frac{1-(1+r)^{-n}}{r}]\\105,000=C[\frac{1-(1+0.00375)^{-360}}{0.00375}]\\105,000=C[197.3612]\\C=532.02[/tex]
So monthly payment would be around $532.02
Now,
With each point purchase, the interest rate goes down by 0.25%, so for 2 points it will be 4.5% - 2(0.25) = 4%
Also, since 20% downpayment, the loan amount would be (0.8)(105,000) = 84,000.
Now, putting these values into the annuity formula we have:
[tex]84,000=C[\frac{1-(1+0.0033)^{-360}}{0.0033}]\\84,000=C(210.4766)\\C=399.09[/tex]
The monthly payment would be around $399.09
The amount that is lower is 532.02 - 399.09 = $132.93
