I'm math challenged today, and apparently google challenged too. Can someone point me to a calculator or check my math/logic to determine the better option in terms of refinancing from a 30 yr fixed to a 15 year fixed (in which payments will increase) vs. investing the difference.

Details:

Current mortgage: 30 year fixed, 4.125%, monthly payment $1842 (just principal and interest), 26 years remaining on mortgage.

Refi mortgage: 15 year fixed, 2.98%, monthly payment $2434 (again, just P&I)

So monthly payment will increase by ~$600, but we'll be paying ~$136K less in interest overall. Using a basic savings calculator starting at $600, contributing $600/month, and assuming 6% market growth for 15 years we'll have ~$176K, and $452K after 26 years (years remaining on mortgage). To really answer this thought I have to figure out the return for the first 15 years (during which we have $600 to invest), and then from years 16-26 when we'll basically be mortgage-free and have the whole amount, right?

This is mortifying (I do a lot of stats as part of my job but this is stumping me today).....refinancing seems the way to go, but I want the clarity of hard numbers before making a move, and right now its a bit fuzzy. Help?