Here is a quick way to get a rough apples-to-apples estimate of the savings from refinancing: compute the principal and interest payment for the new and current interest rate, keeping the balance and term length the same in both computations.
Here's an example:
Open Excel or Google spreadsheet.
Now suppose I can refinance at 5.5% for a 30 year mortgage and suppose I'm already a few years into a 30 year mortgage at 6.25% and I have a current balance of 250000. Suppose it will cost me $2000 to refinance.
Enter the following function:
=PMT(0.0625/12,30*12,250000,0)
This results in a monthly principal and interest payment of $1,539.29/
Here 0.0625 corresponds to my current rate (6.25% per year). 360 corresponds to the length of the mortgage (30 years * 12 payments per year) in my potentially refinanced mortgage. 250000 corresponds to my current balance. This may not correspond to my actual principal and interest payment now because I want to use the same number of payments in both computations to make the comparision fair.
Next, enter the following:
=PMT(0.0550/12,30*12,250000,0)
Here 0.0550 corresponds to my current rate (5.50% per year).
This results in a monthly principal and interest payment of $1,419.47
The savings is $1,539.29-$1,419.47 = $119.82 per month. So, the breakeven point is roughly $2000/$119.82 = 17 months.
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