Todd foley is applying for a $127,000 mortgage. he can get a $787 monthly payment for principal and interest and no points, or a $677 monthly payment with 2.275 points. approximately, how many months will it take todd to cover the cost of the discount points if he takes the lower monthly payment? (round your answer to the nearest whole month.)

Given:
Principal, P=127000
Option A.
A=$787 monthly payment
Option B.
B=$677 monthly payment with 2.275 points.
Question: For option B, how many months before he can recover the cost of discount points, compared with option A.

Solution:

Quick & approximate solution without consideration of time value of money.
Difference=787-677=110 a month
Cost of 2.275 points = 2.275/100*127000=2889.25
Approximate number of months=2889.25/110=26.27 months =>
Approximately, it takes 27 months to recover the cost of points.

We are unable to calculate the exact number of months with consideration of the time value of money because we do not know the given payment of $787 a month applies to what interest rate, or the duration of mortgage. 

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