Todd Foley is applying for a $98,000 mortgage. He can get a $651 monthly payment for principal and interest and no points, or a $541 monthly payment with 2.075 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.)

Accepted Solution

Answer:   18 monthsStep-by-step explanation:The difference in payments is $651 -541 = $110 per month. The cost of the points is ...   $98,000 × 0.02075 = $2033.50So, it will take $2033.50/($110/mo) ≈ 18.48 mo to make up the cost.It will take Todd 18 months to cover the cost of the discount points._____Comment on roundingThe question asks for the answer to be rounded to the nearest whole month. Since the quotient is about 18.486, this rounds to 18. After 18 months, the cost of the points is not quite covered. $53.50 remains to be covered. It isn't until Todd's 19th payment that the cost of points has been fully covered. For "break even" problems such as this one, I prefer to round to the next higher integer, rather than the nearest integer.