You are purchasing a new home and need to borrow $325,000 from a mortgage lender. The mortgage lender quotes you a rate of 6.5% APR for a 30-year fixed rate mortgage (with payments made at the end of each month)
The mortgage lender also tells you that if you are willing to pay one point, they can offer you a lower rate of 6.25% APR for a 30-year fixed rate mortgage. One point is equal to 1% of the loan value. So if you take the lower rate and pay the points, you will need to borrow an additional $3,250 to cover points you are paying the lender. Assuming that you do not intend to prepay your mortgage (pay off your mortgage early), are you better off paying the one point and borrowing at 6.25% APR or just taking out the loan at 6.5% without any points?
Answer: Pay the points!
Points (6.25% APR)
First we need the monthly interest rate = APR / m = 0.0625 / 12 = 0.00520833 or 0.5208%.
Now:
PV = $328,250 ($325,000 + 1 point)
I = 0.5208
FV = 0
N = 360 (30 years × 12 months)
Compute PMT = $2,021.01
No Points (6.5% APR)
First we need the monthly interest rate = APR / m = 0.065 / 12 = 0.005417 or 0.5417%.
Now:
PV = $325,000 (no points)
I = 0.5417
FV = 0
N = 360 (30 years × 12 months)
Compute PMT = $2,054.22
Since $2,021.01 < $2,054.22, pay the points!
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