Final answer:
Carmella can calculate the difference in monthly mortgage payments by computing the payments with and without purchasing points, then subtracting the lower payment from the higher one. This involves using the formula for monthly mortgage payments with the adjusted initial loan amount and interest rates after the 20% down payment and the effect of the points.
Step-by-step explanation:
Carmella is looking at a 30-year mortgage for a $105,000 home with a 4.5% interest rate. With a 20% down payment, her loan amount will be $84,000. If she buys 2 points to lower the interest rate, she pays 2% of her loan amount upfront, which equals to $1,680. Each point typically lowers the interest rate by 0.25%, so her new interest rate would be 4.0%. To calculate the monthly payment, we use the formula for monthly mortgage payments M = P[r(1+r)^n]/[(1+r)^n-1] where M is the monthly payment, P is the principal amount ($84,000), r is the monthly interest rate (0.045/12 or 0.004 for 4.5% and 4% respectively), and n is the number of payments (360).
Without points:
- P = $84,000
- r = 4.5%/12 = 0.00375
- n = 360
- M = $84,000[0.00375(1+0.00375)^360]/[(1+0.00375)^360-1]
With points:
- P = $84,000
- r = 4%/12 = 0.003333
- n = 360
- M = $84,000[0.003333(1+0.003333)^360]/[(1+0.003333)^360-1]
Calculate both monthly payments, subtract the second from the first, and you'll find how much lower the monthly payment will be if Carmella purchases the points.