You'd need to calculate how much you'd be paying over the time you plan on staying in the home for with your current loan vs. if you were to refinance into a new loan.
If you just put down 3.5%, and have a 30-year term, and have only been making the minimum payments, then you'll have to pay the mortgage insurance for a total of 114 payments until your LTV gets to 78% and it'd automatically fall off. So take how many payments you've made (x) and subtract that from 114 (y) and that would equal z, and z * $175 (the mortgage insurance actually decreases little by little every 12 months since it's always based on the new loan amount at the beginning of the year) = how much in mortgage insurance you'd pay over the remaining term of the loan. For example if you've been in the loan for 24 months already (114 minus 24 months = 89 months remaining) that'd be $15,575 more in mortgage insurance (will actually be less since it decreases as I previously mentioned).
Then take the payment difference between your current loan at 3.875% & the new P&I payment at 4.05% (make sure to amortize it over the remaining months in your current loan to compare apples to apples) and multiply that by the remaining months in your current loan to determine how much more in interest savings you'd pay. For example, if it's $25/mo and you've been in the loan for 24 months already (360 minus 24 months = 336 months remaining) then it'd be $8,400 more in interest over that time.
Say you are only in the home for 89 more months, then you'd save the <$15,575 in mortgage insurance while only paying $2,225 more in interest.
Input your actual numbers to determine what your actual savings will be over whatever time period you want to calculate them over.
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