How the rate is set, and why no number appears on this page. Section 6621(a)(2) provides that "The underpayment rate established under this section shall be the sum of (A) the Federal short-term rate determined under subsection (b), plus (B) 3 percentage points." Section 6621(a)(1) sets the overpayment rate at the short-term rate plus 3 points as well, reduced to 2 points for a corporation, and to 0.5 of a point on the portion of a corporate overpayment exceeding $10,000. Subsection (b) then makes the whole thing move: "The Secretary shall determine the Federal short-term rate for the first month in each calendar quarter", that rate "shall apply during the first calendar quarter beginning after such month", and it is determined under section 1274(d) and "rounded to the nearest full percent (or, if a multiple of 1/2 of 1 percent, such rate shall be increased to the next highest full percent)."
So the rate changes four times a year by formula. A page that printed one would be wrong within a quarter. The IRS publishes the current figures on its quarterly interest rates page, and states there that changes "don't affect the interest rate charged for prior quarters or years", which is why a long-running balance can carry several different rates across its life.
The single most valuable sentence in this area is a definitional one. Section 6601(b)(1) provides that the last date prescribed for payment "shall be determined without regard to any extension of time for payment or any installment agreement entered into under section 6159." Both of the things a taxpayer does when they cannot pay are expressly disregarded. An extension of time to file is not an extension of time to pay in the first place, and an extension of time to pay does not stop interest either. Neither does an installment agreement: the arrangement changes when the IRS will accept payment, not when the tax was due. The IRS makes the same point in its own words on its interest page, telling readers that if they enter an installment agreement, "Interest will continue to accrue daily on any amount not paid, including on both penalties and interest."
It compounds daily, with one exception that explains a neighboring page. Section 6622(a) requires that interest "shall be compounded daily". Section 6622(b) then provides that subsection (a) "shall not apply for purposes of computing the amount of any addition to tax under section 6654 or 6655", the estimated-tax additions for individuals and corporations. That carve-out is why published material on estimated taxes correctly describes its charge as not a penalty in the ordinary sense while computing it differently from ordinary interest: the two are calculated by different rules under the same rate.
Interest on penalties has its own start date. Section 6601(e)(2)(A) imposes interest on an assessable penalty, additional amount or addition to the tax "only if such assessable penalty, additional amount, or addition to the tax is not paid within 21 calendar days from the date of notice and demand therefor (10 business days if the amount for which such notice and demand is made equals or exceeds $100,000), and in such case interest shall be imposed only for the period from the date of the notice and demand to the date of payment." The provision expressly excepts the failure-to-file addition under section 6651(a)(1) and the accuracy-related and fraud penalties, which run from the return due date instead. So paying a penalty notice promptly stops interest from ever attaching to most penalties.
It runs both ways, and for an individual the two rates are the same. Section 6611(a) provides that "Interest shall be allowed and paid upon any overpayment in respect of any internal revenue tax at the overpayment rate established under section 6621." Because 6621(a)(1) and (a)(2) both use short-term plus 3 points for a non-corporate taxpayer, an individual is charged and paid at the same rate. A corporation is paid less than it is charged, which is a difference worth knowing and not one this page editorializes about.
Two limits on the overpayment side matter in practice. Section 6611(e)(1) provides that if an overpayment is refunded within 45 days after the last day prescribed for filing the return, determined without regard to extensions, or within 45 days after a late return is actually filed, "no interest shall be allowed". And section 6611(b)(3) provides that on a return filed after its due date, "no interest shall be allowed or paid for any day before the date on which the return is filed." Published material on tax refunds carries the same 45-day rule from the refund side.
One elegant provision that rarely comes up. Section 6621(d) provides that where interest is payable and allowable on equivalent underpayments and overpayments by the same taxpayer for the same period, "the net rate of interest under this section on such amounts shall be zero for such period." Owing and being owed the same amount for the same stretch of time nets to nothing.
Whether it is deductible. Treasury Regulation 1.163-9T, a temporary regulation, provides at paragraph (a) that "No deduction under any provision of Chapter 1 of the Internal Revenue Code shall be allowed for personal interest paid or accrued during the taxable year by a taxpayer other than a corporation", and at paragraph (b)(2)(i)(A) that personal interest includes interest "Paid on underpayments of individual Federal, State or local income taxes and on indebtedness used to pay such taxes ... regardless of the source of the income generating the tax liability." The regulation's own example makes the point that catches people out: an individual who underreports a share of S corporation income and later pays the deficiency plus interest has paid personal interest, "notwithstanding the fact that the additional tax liability may have arisen out of income from a trade or business", and the result "would be the same if A's business had been operated as a sole proprietorship."
Interest the IRS pays you is income. Overpayment interest is taxable in the year it is received, and the IRS reports it to the recipient on a Form 1099-INT. It is reported separately from the refund itself, which is not income.
What can be abated, and what cannot. The IRS states that "We may reduce the amount of interest you owe only if the interest is applied because of an unreasonable error or delay by an IRS officer or employee", with Form 843 as the route, and that where the underlying tax or penalty is reduced by an amended return or by penalty relief, "we'll automatically reduce the related interest." Interest is derivative: it shrinks when the thing it sits on shrinks, and otherwise it does not.