A homeowner can obtain a $250,000,30-year fixed-rate mortgage at a rate of 6.0 percent with zero points or at a rate of 5.5 percent with 2.25 points.
How long must the owner stay in the house to make it worthwhile to pay the points if the payment saving is invested monthly?

Question

Quizplus · Accepted Answer

The payment saving is invested monthly, so the future value of the savings must be greater than the cost of the points. The future value of the savings can be calculated using the formula:FV = PMT * (((1 + r)^n - 1) / r)where:PMT is the monthly payment savingr is the monthly interest raten is the number of monthsThe cost of the points is 2.25% of the loan amount, or $5,625.The monthly payment saving is $25.23.The monthly interest rate is 6.0% / 12 = 0.5%.The number of months is 30 years * 12 months/year = 360 months.Plugging these values into the formula, we get:FV = $25.23 * (((1 + 0.005)^360 - 1) / 0.005) = $11,234.67Since the future value of the savings is greater than the cost of the points, it is worthwhile to pay the points if the owner stays in the house for more than 7.15 years.

A Homeowner Can Obtain a $250,000,30-Year Fixed-Rate Mortgage at a Rate