Exact Underpayment Interest Computation?

[taxcurious2]

This is a nitpicking calculate all the decimal digits kind of question.  I'm wondering if anyone out there

can tell me the exact formula for how the IRS calculates interest on underpayments  and provides

some numerical test values to be sure they are right.

What I've gathered is how the interest rate comes out quarterly as 3%+fed short term rate.  (Reference [1])
and that interest is compounded daily (Reference[2])

That's good enough for an approximation but not an exact computation.
For example one can try to use P(1+r/365)^(number of days)
or  P(1+r/366)^(number of days) in a leap year,  as a guess, but I have no way of knowing
if this is correct.  I can imagine slightly different  other formulas as well.

Anyone out there can tell me and prove convincingly that they have it down to the penny?

[1]  https://www.irs.gov/payments/quarterly-interest-rates

[2]  https://uscode.house.gov/view.xhtml?req=(title:26%20section:6622%20edition:prelim)%20OR%20(granuleid...)

[Opus 17]

I don't have the exact formula, I'm not sure anyone does.

One thing to note is there is also an underpayment penalty of 0.5% per month or partial month.  So if the IRS determined that you owed $1000 as of June 15, and you paid June 16, you would be assessed one day of interest but the full penalty.  And the interest is compounded on the penalty as well as the balance.

Also, I think the interest rate is variable. 

I think the challenge is not the exact formula but how the IRS applies it.  For example, suppose you owe $5000 when you file your return and pay in full on April 15, 2024.  The IRS wants taxes to be paid in quarterly installments or by withholding, so you technically owed $1250 on the previous April 15 2023, June 15, September 15, and January 15.  So you need to take that amount owed from April 16, add the monthly penalty and the daily interest through June 15, then add the new amount owed and keep calculating monthly penalties and daily interest through September 15, then add the new amount for Sept 16, and so on.   It's a complicated moving target.

[Mike9241]

there is a penalty for underpaying estimated taxes form 2210 (see form 2210 and the instructions for the computation of this penalty), a penalty of .5%/month for paying after the normal due date. in addition, when paying after the normal due date there is currently an 8% interest charge which is compounded daily. it consists of the federal short-term interest rate of 5% + an added 3%. the rate changes every 3 months 

https://www.irs.gov/payments/quarterly-interest-rates 

it seems you are asking about the 2210 penalty only 

[taxcurious2]

So nobody knows which formula is used?  surely the IRS knows, at least the person who programmed the computer that charges the interest.  

[Opus 17]

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@taxcurious2 wrote:

So nobody knows which formula is used?  surely the IRS knows, at least the person who programmed the computer that charges the interest.  

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Of course, but you are asking for the exact programming specifications and test values.  We don't have that.  There are other IRS resources, for example:

https://www.irs.gov/irm/part20/irm_20-002-005r

https://www.irs.gov/payments/interest

If you want to know more, you may need to ask an enrolled agent.

[VolvoGirl]

And even if you know the formula and calculations  we don't know all your specific info and dates you made any payments and when the IRS got the payments.  If you have a penalty on 1040 line 38 or want to check the IRS you can fill out form 2210.

You might be able to eliminate it or at least reduce it. You can go to Federal Taxes tab or Personal tab, under Other Tax Situations and select Start by the Underpayment Penalties. You will answer a series of questions that may reduce or eliminate the penalty. Or you can elect to have the IRS figure the penalty for you. It's form 2210.

It's under

Federal or Personal (for Home & Business Desktop)

Other Tax Situations

Additional Tax Payments

Underpayment Penalties - Click the Start or update button

How to add form 2210 for Underpayment Penalty
https://ttlc.intuit.com/community/tax-payments/help/how-do-i-add-form-2210/00/25703

IRS Form 2210
https://www.irs.gov/pub/irs-pdf/f2210.pdf

IRS Form 2210 Instructions
https://www.irs.gov/pub/irs-pdf/i2210.pdf

[taxcurious2]

> And even if you know the formula and calculations  we don't know all your specific info and dates you made any payments and when the IRS got the payments

Now that's just mathematically false.  Firstly when the IRS send out a 2210 there are dates and interest numbers.
Secondly the formula can be applied from date to date, it's fairly simple mathematics, and anyway

readily done in spreadsheets, but one needs to be certain of which of several formulas are applying.

If people would supply me with dates of 2210 notices, the dollar values of the underpayment, and the 

date taxes were due (which I probably can guess), I'm certain I can reverse engineer the formula.
Very likely it's the P(1+r/365)^n. formula, but I'd need data to be sure.   I'd be happy to post the
spreadsheet entry that computes the value to the penny if I can reverse engineer it.

I don't need personal information just the data from the 2210 .  

[taxcurious2]

oh wait i don't mean 2210 i mean the notice irs sends when one fails to pay ones taxes on the 1040 etc

[taxcurious2]

I meant CP2000 forms

[taxcurious2]

Aha success!  For those who thought that the formula was unknowable , I say that's silly and I will

provide a spreadsheet example. For those who worried about the quarterly change in interest rates,

you just compute each quarter one at a time.  My data is a non-leap year, but I'd change 365 to 366 for leap years, and I'm pretty confident that would be right.

I have a CP2000 form that says that on 2021 taxes there is $538 owed of interest on $8964 underreported interest and that it is due April 26, 2023.  I can compute that number $538 based on nothing more than what I just wrote and the published quarterly interest rates.

Here are my computations followed by the formulas in the cells.  The spreadsheet starts in A1 (upper left)
and the interest rate data is published here: https://www.irs.gov/payments/quarterly-interest-rates

One observation is that there is no 0.5% extra in this case.  

RESULT IN BOTTOM RIGHT

Year	Quarter	Int rate	Start Date	End Date	Day Count	1.000000	$8,964
22	2	4%	4/16	6/30	76	1.008363
22	3	5%	7/1	9/30	92	1.021151
22	4	6%	10/1	12/31	92	1.036710
23	1	7%	1/1	3/31	90	1.054757
23	2	7%	4/1	4/26	26	1.060029	$9,502
							$538

FORMULAS with DATA from my example

Year	Quarter	Int rate	Start Date	End Date	Day Count	1.000000	$8,964
22	2	4%	4/16	6/30	=E2-D2+1	=G1*(1+C2/365)^F2
22	3	5%	7/1	9/30	=E3-D3+1	=G2*(1+C3/365)^F3
22	4	6%	10/1	12/31	=E4-D4+1	=G3*(1+C4/365)^F4
23	1	7%	1/1	3/31	90	=G4*(1+C5/365)^F5
23	2	7%	4/1	4/26	=E6-D6+1	=G5*(1+C6/365)^F6	=H1*G6
							=H6-H1