As per the formula given,
Regular monthly payment = P(r/n) /[1-(1+r/n)^-nt]
Here, for Mortgage A,
P = $140,000, r = 6.25%, n = 12, t = 20
Putting values in formula:
140000(6.25%/12) /[1-(1+6.25%/12)^-12x20]
729.1667 /0.712564
1,023.30, so mortgage A monthly payment is $1,023.30 and total payment in EMI will be $1,023.30 x 240 = $245,592
Add: Closing cost = $2100
Add: Points at 1% x 140000 = 14000
Less: principal value = -140000
Total cost of mortgage A = $121,692
For Mortgage B,
P = $140,000, r = 4.5%, n = 12, t = 20
Putting values in formula:
140000(4.5%/12) /[1-(1+4.5%/12)^-12x20]
525 /0.592745
885.71, so mortgage b monthly payment is $885.71 and total payment in EMI will be $885.71 x 240 = $212,570.40
Add: Closing cost = $2100
Add: Points at 4% x 140000 = 56000
Less: principal value = -140000
Total cost of mortgage B = $130,670
Option A is correct , Mortgage B has larger total cost than B by $8,978(130670-121692)
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