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 2points. How much lower will her monthly payment be if she purchases thepoints?

Answer:$132.93Step-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 amountC is the monthly paymentr 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 105,000C is what we need to findr is the 0.045/12 = 0.00375n is 12*30 = 360Now, 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 $532.02Now,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 $399.09The amount that is lower is  532.02 - 399.09 = $132.93