To evaluate two options, we need to subtract the monthly payments and the rebate (amount paid by the lender towards the closing costs).
In our example:
Rebate difference = $4,566
Monthly payment = $45
Tax adjustment = $34
$4,566 / $34 = $134.29
$134.29 / 12 months = 11.19 years to break even
It will take over 11 years to have the benefit of a lower rate. At the same time, if the extra $4,000 is used to pay off a credit card at 22% or even take a vacation, the benefit of the higher rate with the bigger rebate will be even more significant. For different folks—different strokes.
Cheers,