What is the interest and penalty for a late payment to the IRS

Interest compounds daily. Per the IRS, interest accrues on any unpaid tax from the due date of the return until the date of payment in full. The interest rate is determined quarterly (but compounded daily) and is the federal short-term rate plus 3 percent.  Please see the IRS link Newsroom Search for the current quarterly interest rate on underpayments.

In addition, if you file a return but don't pay all tax owed on time, you'll generally have to pay a late payment penalty. The failure-to-pay penalty is one-half of one percent for each month, or part of a month, up to a maximum of 25%, of the amount of tax that remains unpaid from the due date of the return until the tax is paid in full. The one-half of one percent rate increases to one percent if the tax remains unpaid 10 days after the IRS issues a notice of intent to levy property. If you file your return by its due date and request an installment agreement, the one-half of one percent rate decreases to one-quarter of one percent for any month in which an installment agreement is in effect. Be aware that the IRS applies payments to the tax first, then any penalty, then to interest. Any penalty amount that appears on your bill is generally the total amount of the penalty up to the date of the notice, not the penalty amount charged each month.

Topic No. 653 IRS Notices and Bills, Penalties, and Interest Charges

"Failure to pay tax reported on return: Internal Revenue Code §6651(a)(2)

• 0.5% of tax not paid by due date, April 15; 0.25% during approved installment agreement (if return was filed on time, and taxpayer is an individual); 1% if tax is not paid within 10 days of a notice of intent to levy
• Recurring charge on the remaining unpaid tax each month or part of a month following the due date, until the tax is fully paid or until 25% is reached
• Full monthly charge applies, even if the tax is paid before the month ends"

This is simple interest, not compound interest.