Question

Carmella is purchasing a $105,000 home and her bank is offering her a 30-

Answer 1

Answer:

$132.93

Step-by-step explanation:

We will use annuity formula, which is:

$P=C[\frac{1-(1+r)^{-n}}{r}]$

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:

$P=C[\frac{1-(1+r)^{-n}}{r}]\\105,000=C[\frac{1-(1+0.00375)^{-360}}{0.00375}]\\105,000=C[197.3612]\\C=532.02$

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:

$84,000=C[\frac{1-(1+0.0033)^{-360}}{0.0033}]\\84,000=C(210.4766)\\C=399.09$

The monthly payment would be around $399.09

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