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Did you ask the first lender if they could match the rate?
Ok I busted out the calculator on this one. I may be slightly off, but you will get the idea. Remember, interest is tax deductible - PMI is not.
If you go with the 3.875 you will be done with PMI in July 2018ish.
If you go with the 3.675 you will be done with PMI in December 2021ish.
That's a gap of 41 months - about.
If you went 3.875 you would have spent an additional 2,050 on interest, but saved 3,280 on PMI. To make up that difference, you would have to hold the 3.675 loan for another 5 years 6 months. You wouldn't break even on the savings in interest until 2026.
FWIW - Interest difference between 3.675 and 3.875 on a 311k loan is about $50 a month.