Carmella is purchasing a $105,000 home and her bank is offering her a 30-
year mortgage at a 4.5% interest rate. in order to lower her monthly payment,
carmella will make a 20% down payment and is considering a purchase of 2
points. how much lower will her monthly payment be if she purchases the
points?

$132.93

Step-by-step explanation:

We will use annuity formula, which is:

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:

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:

The monthly payment would be around $399.09

The amount that is lower is  532.02 - 399.09 = $132.93

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