Dear Dr. Don,
I have a mortgage balance of $178,000 with 149 payments left at 5.5%. I'm thinking about refinancing for 15 years at 4.25% with no fees, or 3.875% with $3,000 in closing fees. I don't know if it's worth it to refinance now.
-- Vicky Vacillates

Dear Vicky,
With only 149 payments to go -- that's 12 years and five months -- refinancing with a 15-year mortgage has you extending your loan term. You'll still realize some interest savings by refinancing, as shown in the table below, but you can improve on this approach to refinancing.

Mortgage refinance options
 Refi with no closing costsRefi with closing costsExisting first mortgage
Loan balance:$ 178,000.00$ 181,000.00$ 178,000.00
Interest rate:4.250%3.875%5.500%
Loan term (months):180180149
Mortgage payment:$ 1,339.06$ 1,327.53$ 1,651.25
Total interest:$ 63,030.00$ 57,954.60$ 68,036.46
Pretax savings vs. existing mortgage:$ 5,006.46$ 10,081.87 
Estimated after-tax savings at 25%:$ 3,754.84$ 7,561.40 

Assuming you can afford your current payment, what I would suggest is to refinance and then make additional principal payments on the new mortgage each month equal to the difference between the new monthly mortgage payment and the old mortgage payment. You'll shorten the life of your mortgage and by doing so, capture additional interest savings, as shown in the following table:

Refinance with additional principal payments
 Refi with no closing costsRefi with closing costsExisting first mortgage
Loan balance:$ 178,000.00$ 181,000.00$ 178,000.00
Interest rate:4.250%3.875%5.500%
Loan term (months):137180149
Mortgage payment:$ 1,339.06$ 1,327.53$ 1,651.25
Additional principal payment:$ 312.19$ 323.72$ 0.00
Total monthly payment:$ 1,651.25$ 1,651.25$ 1,651.25
Total interest:$ 46,615.43$ 42,770.43$ 68,036.46
Pretax savings vs. existing mortgage:$ 21,421.03$ 25,266.03 
Estimated after-tax savings at 25%:$ 16,065.77$ 18,949.52 

I made the assumption that you financed the $3,000 in closing costs, but you could bring cash to closing. The estimated after-tax savings assumes that you can fully utilize the mortgage interest deduction and that it doesn't just replace the standard deduction on your federal income taxes. The biggest assumption, however, is that you don't plan to move anytime soon.

I constructed the tables using Bankrate's mortgage calculator. Bankrate also has several mortgage refinance calculators on its website that will help you calculate the interest savings.