Answer:
$132.93
Step-by-step explanation:
We will use annuity formula, which is:
![P=C[\frac{1-(1+r)^{-n}}{r}]](https://tex.z-dn.net/?f=P%3DC%5B%5Cfrac%7B1-%281%2Br%29%5E%7B-n%7D%7D%7Br%7D%5D)
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:
![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](https://tex.z-dn.net/?f=P%3DC%5B%5Cfrac%7B1-%281%2Br%29%5E%7B-n%7D%7D%7Br%7D%5D%5C%5C105%2C000%3DC%5B%5Cfrac%7B1-%281%2B0.00375%29%5E%7B-360%7D%7D%7B0.00375%7D%5D%5C%5C105%2C000%3DC%5B197.3612%5D%5C%5CC%3D532.02)
So <u>monthly payment would be around $532.02</u>
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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:
![84,000=C[\frac{1-(1+0.0033)^{-360}}{0.0033}]\\84,000=C(210.4766)\\C=399.09](https://tex.z-dn.net/?f=84%2C000%3DC%5B%5Cfrac%7B1-%281%2B0.0033%29%5E%7B-360%7D%7D%7B0.0033%7D%5D%5C%5C84%2C000%3DC%28210.4766%29%5C%5CC%3D399.09)
The <u>monthly payment would be around $399.09</u>
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The amount that is lower is 532.02 - 399.09 = $132.93