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If you pay an additional $908 per month on existing loan, then you will owe $323,668 after 7 years of payments from this point. If you get the 15 Yr at 4% and no closing costs, then you will make the same payment ( $3580) and owe $259K after 7 years.
This makes a lot of sense. You are paying around $2000 a month in interest and that would drop to $1600-ish at close. At your current payment schedule, you would pay around $260,000 in interest. With the new loan, that amount shrinks to about $199,000 over the life of the loans. So over the 7-10 years, you should be saving 10s of thousands of dollars...and remember, that's at no cost to you.
Sounds like a no-brainer to me. The only concern would be if the mandatory commitment to the 15 year payment could cause problem in the future if there was an unexpected loss or reduction in income. Since you mention secure and stable income, that seems a non-factor.
The math has already been done well in this thread. Realize that a portion of that effective savings would be reduced when you factor in a lower tax deduction each year with declining interest, but as long as you getting a no cost refinance, even a small reduction in rate is worthwhile.
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