How long must a homeowner stay in the house to break even after paying $3,000 in closing costs for a refinancing that saves them $100 per month?

To determine how long a homeowner must stay in the house to break even after paying $3,000 in closing costs for a refinancing that saves them $100 per month, you first need to look at the total savings accrued each month and how those savings compare to the initial costs incurred.

The monthly savings of $100 means that over a certain number of months, the cumulative savings will eventually equal the closing costs. To find the break-even point, you divide the total closing costs by the monthly savings.

In this case, the calculation is: $3,000 (closing costs) ÷ $100 (monthly savings) = 30 months.

This calculation gives you a break-even point slightly above 30 months, as you accumulate savings each month. Since rounding can sometimes lead to an exact number that might not represent the correct time period to fully cover the upfront costs, in financial terms, you typically round up to account for any partial months, and this results in a requirement of approximately 31.66 months.

Thus, the correct answer of 31.66 months accurately reflects the break-even point when considering the expenses needed to be recouped through refinancing savings.