George4Tacks
Level 15
Tuesday

FYI - George has a MS in Mathematics Education. George knows how to do simultaneous equations. George know you ain't gonna get an exact answer in this iterative calculation that involves both of your key numbers changing as you try to work it out. IRS knows you ain't gonna get an exact answer in this iterative calculation that involves both of your key numbers changing as you try to work it out. Get close and plug that number in.

I got this using AI with Google, maybe it will help:

Setting up the simultaneous equations 
The following equations can be used to solve this issue. For a single filer, the taxable portion of Social Security benefits is determined by a series of thresholds. For this example, we will focus on the maximum 85% inclusion amount. 
Variables: 
  •  

     

    AGIprecap A cap G cap I sub p r e end-sub
    π΄πΊπΌπ‘π‘Ÿπ‘’
    : AGI before the NOL deduction.
  •  

     

    SStotalcap S cap S sub t o t a l end-sub
    π‘†π‘†π‘‘π‘œπ‘‘π‘Žπ‘™
    : The total Social Security benefits received (from Form SSA-1099, Box 5).
  •  

     

    SStaxablecap S cap S sub t a x a b l e end-sub
    π‘†π‘†π‘‘π‘Žπ‘₯π‘Žπ‘π‘™π‘’
    : The taxable portion of Social Security benefits.
  •  

     

    AGIcap A cap G cap I
    𝐴𝐺𝐼
    : The final AGI after all adjustments.
  •  

     

    NOLfullcap N cap O cap L sub f u l l end-sub
    𝑁𝑂𝐿𝑓𝑒𝑙𝑙
    : The full NOL carryforward amount.
  •  

     

    NOLdeductcap N cap O cap L sub d e d u c t end-sub
    𝑁𝑂𝐿𝑑𝑒𝑑𝑒𝑐𝑑
    : The NOL deduction for the current year. 
Equation 1: Calculating the maximum NOL deduction
The maximum NOL deduction allowed is 80% of your taxable income without the NOL deduction. For a simple case (assuming the standard deduction), this can be expressed as:
 

 

NOLdeduct=0.80Γ—(AGIpre+SStaxableβˆ’Standard Deduction)cap N cap O cap L sub d e d u c t end-sub equals 0.80 cross open paren cap A cap G cap I sub p r e end-sub plus cap S cap S sub t a x a b l e end-sub minus Standard Deduction close paren
𝑁𝑂𝐿𝑑𝑒𝑑𝑒𝑐𝑑=0.80Γ—(π΄πΊπΌπ‘π‘Ÿπ‘’+π‘†π‘†π‘‘π‘Žπ‘₯π‘Žπ‘π‘™π‘’βˆ’Standard Deduction)
Equation 2: Calculating taxable Social Security benefits (85% rule)
The taxable portion of Social Security benefits is the lesser of two amounts, but the primary factor is your combined income (AGI + nontaxable interest + 50% of benefits). For combined income over the top threshold ($34,000 for single,
 

 

44,000formarriedfilingjointly),thetaxableamountistypically8544 comma 000 f o r m a r r i e d f i l i n g j o i n t l y close paren comma t h e t a x a b l e a m o u n t i s t y p i c a l l y 85
44,000π‘“π‘œπ‘Ÿπ‘šπ‘Žπ‘Ÿπ‘Ÿπ‘–π‘’π‘‘π‘“π‘–π‘™π‘–π‘›π‘”π‘—π‘œπ‘–π‘›π‘‘π‘™π‘¦),π‘‘β„Žπ‘’π‘‘π‘Žπ‘₯π‘Žπ‘π‘™π‘’π‘Žπ‘šπ‘œπ‘’π‘›π‘‘π‘–π‘ π‘‘π‘¦π‘π‘–π‘π‘Žπ‘™π‘™π‘¦85
 

 

SStaxable=0.85Γ—SStotalcap S cap S sub t a x a b l e end-sub equals 0.85 cross cap S cap S sub t o t a l end-sub
π‘†π‘†π‘‘π‘Žπ‘₯π‘Žπ‘π‘™π‘’=0.85Γ—π‘†π‘†π‘‘π‘œπ‘‘π‘Žπ‘™
 

 

However,thisisonlytrueifyourincomeishighenough.Amorepreciseequation(ignoringnonβˆ’taxableinterestforsimplicity)is∢cap H o w e v e r comma t h i s i s o n l y t r u e i f y o u r i n c o m e i s h i g h e n o u g h point cap A m o r e p r e c i s e e q u a t i o n open paren i g n o r i n g n o n minus t a x a b l e i n t e r e s t f o r s i m p l i c i t y close paren i s colon
π»π‘œπ‘€π‘’π‘£π‘’π‘Ÿ,π‘‘β„Žπ‘–π‘ π‘–π‘ π‘œπ‘›π‘™π‘¦π‘‘π‘Ÿπ‘’π‘’π‘–π‘“π‘¦π‘œπ‘’π‘Ÿπ‘–π‘›π‘π‘œπ‘šπ‘’π‘–π‘ β„Žπ‘–π‘”β„Žπ‘’π‘›π‘œπ‘’π‘”β„Ž.π΄π‘šπ‘œπ‘Ÿπ‘’π‘π‘Ÿπ‘’π‘π‘–π‘ π‘’π‘’π‘žπ‘’π‘Žπ‘‘π‘–π‘œπ‘›(π‘–π‘”π‘›π‘œπ‘Ÿπ‘–π‘›π‘”π‘›π‘œπ‘›βˆ’π‘‘π‘Žπ‘₯π‘Žπ‘π‘™π‘’π‘–π‘›π‘‘π‘’π‘Ÿπ‘’π‘ π‘‘π‘“π‘œπ‘Ÿπ‘ π‘–π‘šπ‘π‘™π‘–π‘π‘–π‘‘π‘¦)π‘–π‘ βˆΆ
 

 

AGI+0.5Γ—SStotal=Combined Incomecap A cap G cap I plus 0.5 cross cap S cap S sub t o t a l end-sub equals Combined Income
𝐴𝐺𝐼+0.5Γ—π‘†π‘†π‘‘π‘œπ‘‘π‘Žπ‘™=Combined Income
$
The taxable benefit formula is based on this combined income and is not a simple linear equation. Because of this, it can be simpler to use an iterative process or to follow the IRS worksheets carefully. 
Using an iterative method (trial-and-error) 
Since the formulas are not perfectly linear, many tax professionals use an iterative or trial-and-error method to arrive at the correct figures. 
  1. Step 1: Initial Calculation (Ignore NOL)
    • Complete the Form 1040 up to the AGI line, but do not include the NOL deduction yet.
    • Calculate the taxable Social Security benefits using the standard IRS worksheets (found in Publication 915). This will give you a preliminary taxable Social Security number.
    • Determine your AGI and taxable income based on this preliminary number.
  2. Step 2: Calculate the NOL Deduction Limit
    • Using the taxable income from Step 1, calculate the maximum allowable NOL deduction (80% for NOLs after 2017).
    • If your full NOL carryover is less than this 80% limit, your NOL deduction is the full amount of the NOL. If it is more, your NOL deduction is limited to the 80% figure.
  3. Step 3: Recalculate with the NOL
    • Enter the calculated NOL deduction from Step 2 onto your Form 1040 (on Schedule 1).
    • This will reduce your AGI and may change your combined income, which in turn could lower the taxable portion of your Social Security benefits.
    • If the taxable Social Security benefits change, the NOL deduction limit might also change.
  4. Step 4: Repeat until it converges
    • Repeat Steps 2 and 3 using the new figures. Continue this process until the numbers stabilize and no longer change. This may only take a few iterations, as noted by tax professionals online. 
Simplified example 
  • Filing Status: Single
  • Other Income: $40,000
  • Total Social Security Benefits (
     

     

    SStotalcap S cap S sub t o t a l end-sub
    π‘†π‘†π‘‘π‘œπ‘‘π‘Žπ‘™
    😞 $20,000
  • NOL Carryover (
     

     

    NOLfullcap N cap O cap L sub f u l l end-sub
    𝑁𝑂𝐿𝑓𝑒𝑙𝑙
    😞 $30,000 
Iteration 1: 
  • Combined Income (no NOL): $40,000 (AGI) + $0 (Interest) + $10,000 (0.5 * SS) = $50,000.
  • Taxable Social Security (from Worksheet): Since combined income > $34,000,
     

     

    SStaxablecap S cap S sub t a x a b l e end-sub
    π‘†π‘†π‘‘π‘Žπ‘₯π‘Žπ‘π‘™π‘’
    = 85% of $20,000 = $17,000.
  • AGI (no NOL): $40,000 + $17,000 = $57,000.
  • Taxable Income (no NOL): $57,000 - $14,600 (2024 standard deduction) = $42,400.
  • Max NOL Deduction: 80% of $42,400 = $33,920.
  • NOL Deduction for Year: The full $30,000 is less than the limit, so $NOL_{deduct} = $30,000. 
Iteration 2 (using NOL deduction of $30,000): 
  • New AGI: $57,000 - $30,000 = $27,000.
  • New Combined Income: $27,000 + $10,000 (0.5 * SS) = $37,000.
  • New Taxable Social Security: The new combined income is between $34,000 and $44,000, so the taxable amount is calculated using the worksheet. It will be lower than the initial $17,000. For instance, it might now be $15,000.
  • New Taxable Income: ($40,000 + $15,000 - $30,000) - $14,600 = $10,400.
  • New Max NOL Deduction: 80% of $10,400 = $8,320.
  • NOL Deduction for Year: This calculation shows that the deduction is limited to $8,320, not the full $30,000. 
You would continue iterating from this point until the change is minimal. This highlights why simultaneous equations (or an iterative process) are necessary to solve the circular reference. 
 
Sorry, the copy and paste did not do the formatting necessary. You can try this search on Chrome "simultaneous equations and social security income with NOL on a 1040"

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