Withholding Problem

My son has gotten himself into an under-withholding situation for 2017. For many years, he claimed four exemptions on his paycheck even though he was single because he had very large deductions from mortgage, tax and
rental loss expenses. He never had any penalty problems on his return because his withholding was always at least 90% of his taxes owed. In late 2016 he sold the rental property and had a large tax bill for 2016 due mainly to having to pay tax on depreciation reclaimed. But again there was no penalty because the withholding he had done in 2016 was more than the taxes he had owed in 2015.
In early 2017, a couple of months after the rental house was sold, he got married and changed his payroll withholding exemptions from single to married. But he left the exemptions alone at four because he incorrectly thought he would still have significant deductions from the mortgage and taxes on a new home and from expected medical expenses, which did not happen. At the end of 2017, he did a dummy tax run for himself and his wife filing jointly and was shocked to realize that they were going to owe the IRS around $3400 in taxes for 2017. The higher than expected amount was mainly a result of him having claimed four exemptions for most of the year and maybe partly also for the fact that he and his wife together were now in a tax bracket where some of his deductions (like mortgage insurance) weren't allowed.
He has now changed his exemptions back to married one for 2018, so their taxes for 2018 and thereafter should be ok. But for 2017, he and his wife will owe a net of $3400 and there will be a penalty because the amount they both withheld in 2017 (which totaled $17,352) was lower than their combined tax liability for 2016 (which was $24,645), which was the year he sold his rental property. Their combined withholding of $17,352 is also less than 90% of their total $20,709 tax liability for 2017.
So the question is...what, if anything, does he do now in January 2018? He has already changed his exemptions to where they should be, so this problem should not reoccur. Should he just do nothing until he files his taxes in April 2018 and then pay the penalty at that time? Or should he file some kind of estimated taxes now in January or do some kind of pre-payment to reduce the amount of the penalty? Or is there a way he can get an exemption from the IRS for the penalty, since it was a one-time event caused by his failure to end his previous withholding arrangement which was tied with his rental expenses?
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On Thursday, January 11, 2018 at 11:22:07 AM UTC-8, Fred wrote:

If he pays the 4th quarter estimated taxes (90% of total taxes due, less withholding) by January 15, the 4th quarter estimated tax penalty will be $0. Otherwise, he could just pay the taxes in April. If he requests the IRS calculate the estimated tax penalty (which they will probably do correctly), he need only pay the penalty when he gets a bill.
-- Arthur Rubin, AFSP, CRTP, Brea, CA
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On 1/11/2018 11:20 AM, Fred wrote:

Based on your information and a bit of reading between the lines (which I am not always good at), I calculate your penalty as a whopping $34. If you make a payment now (as suggested by Arthur), rather than waiting for April 15, you may shave about $13 off of that penalty.
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Agree. Make your Q4 estimated payment this week. Might want to look at the annualized income method to see if your penalty is reduced. You also have the option of claiming witholding when paid or averaged (doubt it makes a difference in this case; might have helped if he adjusted his witholding before the end of 2017).
scott s. ..
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