This equation will do an Amortization and calculate the number of months it will take to recoup the cost if you buy Points up front.  Points can provide a lower interest rate which can possibly provide savings over the life of the loan.

Discount points are payments made up-front to obtain lower interest rates. A lender can usually quote mortgage rates and provide payment information regarding zero, one, or two points. Buyinga lower interest rate with discount points could be a cost effective way of lower the Total mortgage Cost.

This equation will calculate the total interest saved on loan if the Points are purchased, and will also calculate (at the new interest rate) how many months it will take  to recover,  in savings,  the cost of the Points.

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Notes

This equation is used to answer questions of the form:

If I buy points before closing;  How many months will it take to recoup the expense ?

Purchasing discount points allows the Homeowner to get a lower interest rate.  The 'Points' are subtracted from the interest rate..