Question

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?

Answer 1

Explanation:

12.39

Answer 2

$132.93

Explanation:

We will use annuity formula, which is:

`P=C[(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[(1-(1+r)^(-n))/(r)]\\105,000=C[(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[(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