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Can a custodian refuse prior-year IRA/HSA deposit postmarked April 15?
The "must be postmarked" language might be just from the old bank itself, not from the IRS.  The language I see in Publication 969 only says "You can make contributions to your HSA for 2014 until April 15, 2015." In this case, it is understandable that the credit union you have the new account with does not want to accept the contribution for tax year 2014.  You didn't have an account with them in 2014.  You didn't even send out the paperwork to them to open the account until last week, and they didn't open your account until this week, after the deadline. It is unfortunate, but I don't think you'll be able to force them to do anything differently here.  It is just too late. I do know how that feels.  I had a somewhat similar circumstance with my HSA, the first year I had the account.  I contributed money to the HSA using my credit union's website, transferring money from my checking account into my HSA, as I was told to do.  In January and February of the following year, I made more contributions this way, thinking that I was making them for the previous tax year.  However, they never got coded correctly by the credit union, and I later found out that the credit union counted those as contributions for the current year.  As a result, I was essentially denied the full contribution limit for that year, and had a bit of a paperwork nightmare.  Now, if I have to make a prior year contribution, I only make it in person, and they have a form they have me fill out each time I do.