Last year I did a sizable backdoor roth conversion in the 4th quarter and the next day I sent an electronic payment to the IRS for the estimated tax on the conversion using non-IRA funds. After filing, the IRS penalized me for tax underpayment even though I got a significant refund at the final filing. All I could get out of them is that I didn't file the right paperwork (1022 maybe?). Anyway, what is the proper procedure for making an estimated tax payment on a sizeable backdoor roth conversion.
