Question

ashlee is purchasing a $125,000 home and her bank is offering her a 30-year mortgage at a 4.75% interest rate. in order to lower her monthly payment, ashlee 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?

a. $16.69

b. $14.96

c. $15.98

d. $12.09

Explanation:

Step1: Calculate loan amount

Down payment = 20% of $125,000 = $25,000
Loan amount = $125,000 - $25,000 = $100,000

Step2: Monthly rate without points

Annual rate = 4.75% = 0.0475
Monthly rate \( r_1 = \frac{0.0475}{12} \approx 0.00395833 \)
Number of payments \( n = 30 \times 12 = 360 \)

Step3: Monthly payment without points

Formula: \( M = P \times \frac{r(1+r)^n}{(1+r)^n - 1} \)
\( M_1 = 100000 \times \frac{0.00395833(1+0.00395833)^{360}}{(1+0.00395833)^{360} - 1} \approx 521.65 \)

Step4: Rate with 2 points

1 point = 0.25% rate reduction, so 2 points = 0.5% reduction
New annual rate = 4.75% - 0.5% = 4.25% = 0.0425
New monthly rate \( r_2 = \frac{0.0425}{12} \approx 0.00354167 \)

Step5: Monthly payment with points

\( M_2 = 100000 \times \frac{0.00354167(1+0.00354167)^{360}}{(1+0.00354167)^{360} - 1} \approx 504.96 \)

Step6: Difference in payments

\( M_1 - M_2 = 521.65 - 504.96 = 16.69 \)

Answer:

A. $16.69