Question

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Lenny and Lisa have obtained a 30-year, fixed rate mortgage for $675,250 with a 7.25% interest rate. They purchased 3 points and their rate is now 6.875%. Factoring in the cost of points, when is the break-even point on their mortgage? (2 points)
3 years, 4 months
4 years, 5 months
8 years, 7 months
9 years, 11 months

Answer 1

To calculate the break-even point on their mortgage, we need to determine how long it will take for the savings from the lower interest rate to offset the cost of purchasing the points.

First, let's calculate the monthly payment for the original mortgage:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]

where:
P = principal amount = $675,250
i = monthly interest rate = 7.25% / 12 = 0.6042%
n = total number of payments = 30 years * 12 months per year = 360

M = $4,652.67

Next, let's calculate the monthly payment for the mortgage with the lower rate and the cost of points:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]

where:
P = principal amount = $675,250 - (3 points * $6,752.50 per point) = $655,992.50
i = monthly interest rate = 6.875% / 12 = 0.5729%
n = total number of payments = 30 years * 12 months per year = 360

M = $4,332.87

The monthly savings from the lower interest rate is:

$4,652.67 - $4,332.87 = $319.80

The cost of the points is:

3 points * $6,752.50 per point = $20,257.50

The break-even point is the number of months it will take for the savings to equal the cost of the points:

$20,257.50 / $319.80 per month = 63.3 months

So the break-even point is approximately 63.3 months, which is:

5 years and 3 months

Therefore, the answer is not one of the given options.