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01 The demo
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Levered IRR, $7M deal, 5-yr hold open ▾
TrueMath
Public Library ▾
···
A $7M deal: NOI 450K growing 3%, 5-year hold…
▤ CRE Acquisitions Analyst simulation ╃ Scenarios↗ Share
Chat · Natural LanguageRequest
A 7,000,000 deal: NOI 450,000 growing 3%, 5-year hold, 65% LTV at 7% on 30-year am, closing 1.5%, exit cap 6.5%, selling costs 2%. What's my levered IRR?
ENGINE INPUT (LANGUAGE MODEL INTERPRETATION)
property_value: 7000000 USD
noi: 450000 USD
noi_growth_rate: 3%
hold_period_years: 5 yr
ltv_ratio: 65%
note_rate: 7%
loan_term_months: 360
closing_cost_rate: 1.5%
exit_cap_rate: 6.5%
selling_cost_rate: 2%
calculate: irr_result
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Jul 9, 2026 9:12 AMResponse
Creating Scenario 1.

Loan Amount from LTV

Calculates loan amount, property value, or LTV ratio given the other two values.
• Property Value / Purchase Price: $7,000,000
• Loan-to-Value Ratio (LTV): 65.0%
• Loan Amount: $4,550,000

Hold Period in Months

Expresses the hold period in months for the loan payoff calculation.
• Hold Period (Years): 5 yr
• Hold Period (Months): 60

Loan Payoff at Sale

Calculates the remaining loan balance at the end of the hold period.
• Hold Period (Months): 60
• Loan Amount: $4,550,000
• Interest Rate (Note Rate): 7.00%
• Loan Amortization Term (Months): 360
• Loan Payoff at Sale: $4,282,987

Hold Period as Scalar Years

Expresses the hold period as a bare number of years for use as a loop bound and in series index arithmetic.
• Hold Period (Years): 5 yr
• Hold Period (Scalar Years): 5

Projected NOI Series

Projects NOI year-by-year over the hold period at a compound annual growth rate.
• Hold Period (Scalar Years): 5
• Net Operating Income (NOI): $450,000
• NOI Growth Rate (Annual): 3.0%
• Projected NOI Series:
#NOI
1$450,000
2$463,500
3$477,405
4$491,727
5$506,479

Terminal / Reversion Value

Calculates the projected sale price at end of hold period by applying the exit cap rate to Year N+1 NOI, where the year-after-exit growth is taken from the final-period growth of the projected NOI series itself.
• Exit Cap Rate: 6.50%
• Projected NOI Series: See table above
• Terminal / Reversion Value: $8,025,744

Net Sale Proceeds

Calculates net proceeds from sale after selling costs and loan payoff.
• Terminal / Reversion Value: $8,025,744
• Selling Cost Rate: 2.0%
• Loan Payoff at Sale: $4,282,987
• Net Sale Proceeds: $3,582,241

Annual Debt Service

Calculates annual debt service, or back-solves loan amount or note rate, based on loan terms.
• Loan Amount: $4,550,000
• Interest Rate (Note Rate): 7.00%
• Loan Amortization Term (Months): 360
• Annual Debt Service: $363,255

Annual Cash Flows Series

Builds a year-by-year table of pre-tax cash flows over the hold period.
• Hold Period (Scalar Years): 5
• Projected NOI Series: See table above
• Annual Debt Service: $363,255
• Annual Cash Flows Series:
#Cash Flow
1$86,745
2$100,245
3$114,150
4$128,472
5$143,224

Terminal Year Cash Flow

Calculates the total cash flow in the final hold year, combining operating cash flow and net sale proceeds.
• Annual Cash Flows Series: See table above
• Net Sale Proceeds: $3,582,241
• Terminal Year Cash Flow: $3,725,465

Closing Costs

Calculates closing costs as a percentage of property value.
• Property Value / Purchase Price: $7,000,000
• Closing Cost Rate: 1.5%
• Closing Costs: $105,000

Equity Required

Calculates equity required as purchase price minus loan proceeds plus closing costs.
• Loan Amount: $4,550,000
• Property Value / Purchase Price: $7,000,000
• Closing Costs: $105,000
• Equity Required: $2,555,000

IRR Cash Flow Vector

Constructs the full IRR cash flow vector: initial equity outflow, annual operating cash flows, and terminal year cash flow.
• Equity Required: $2,555,000
• Annual Cash Flows Series: See table above
• Hold Period (Scalar Years): 5
• Terminal Year Cash Flow: $3,725,465
• IRR Cash Flow Vector:
#Cash Flow
0$-2,555,000
1$86,745
2$100,245
3$114,150
4$128,472
5$3,725,465

Internal Rate of Return

Calculates the levered IRR from the full hold period cash flow vector.
• IRR Cash Flow Vector: See table above
• Internal Rate of Return (IRR): 10.85%
Requested result for Internal Rate of Return (IRR) is 10.85%.
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Equity payback chart, $7.2M deal open ▾
TrueMath
Public Library ▾
···
NOI 484,800, price 7,200,000 — the equity payback…
▤ CRE Acquisitions Analyst simulation ╃ Scenarios↗ Share
Chat · Natural LanguageRequest
NOI 484,800, price 7,200,000, 65% LTV at 7% on 30-year am, closing 1.5%, NOI grows 3%, 5-year hold, exit cap 6.5%, selling 2%. Show me the equity payback chart.
ENGINE INPUT (LANGUAGE MODEL INTERPRETATION)
noi: 484800 USD
property_value: 7200000 USD
ltv_ratio: 65%
note_rate: 7%
loan_term_months: 360
closing_cost_rate: 1.5%
noi_growth_rate: 3%
hold_period_years: 5 yr
exit_cap_rate: 6.5%
selling_cost_rate: 2%
calculate: cumulative_return_chart
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Jul 9, 2026 11:36 AMResponse
Creating Scenario 1.

Closing Costs

Calculates closing costs as a percentage of property value.
• Property Value / Purchase Price: $7,200,000
• Closing Cost Rate: 1.5%
• Closing Costs: $108,000

Loan Amount from LTV

Calculates loan amount, property value, or LTV ratio given the other two values.
• Property Value / Purchase Price: $7,200,000
• Loan-to-Value Ratio (LTV): 65.0%
• Loan Amount: $4,680,000

Equity Required

Calculates equity required as purchase price minus loan proceeds plus closing costs.
• Loan Amount: $4,680,000
• Property Value / Purchase Price: $7,200,000
• Closing Costs: $108,000
• Equity Required: $2,628,000

Hold Period as Scalar Years

Expresses the hold period as a bare number of years for use as a loop bound and in series index arithmetic.
• Hold Period (Years): 5 yr
• Hold Period (Scalar Years): 5

Equity Invested Reference Series

Builds a flat reference line equal to the equity invested in every year of the hold.
• Hold Period (Scalar Years): 5
• Equity Required: $2,628,000
• Equity Invested Reference Series:
#Equity Invested
1$2,628,000
2$2,628,000
3$2,628,000
4$2,628,000
5$2,628,000

Annual Debt Service

Calculates annual debt service, or back-solves loan amount or note rate, based on loan terms.
• Loan Amount: $4,680,000
• Interest Rate (Note Rate): 7.00%
• Loan Amortization Term (Months): 360
• Annual Debt Service: $373,634

Projected NOI Series

Projects NOI year-by-year over the hold period at a compound annual growth rate.
• Hold Period (Scalar Years): 5
• Net Operating Income (NOI): $484,800
• NOI Growth Rate (Annual): 3.0%
• Projected NOI Series:
#NOI
1$484,800
2$499,344
3$514,324
4$529,754
5$545,647

Hold Period in Months

Expresses the hold period in months for the loan payoff calculation.
• Hold Period (Years): 5 yr
• Hold Period (Months): 60

Loan Payoff at Sale

Calculates the remaining loan balance at the end of the hold period.
• Hold Period (Months): 60
• Loan Amount: $4,680,000
• Interest Rate (Note Rate): 7.00%
• Loan Amortization Term (Months): 360
• Loan Payoff at Sale: $4,405,358

Terminal / Reversion Value

Calculates the projected sale price at end of hold period by applying the exit cap rate to Year N+1 NOI, where the year-after-exit growth is taken from the final-period growth of the projected NOI series itself.
• Exit Cap Rate: 6.50%
• Projected NOI Series: See table above
• Terminal / Reversion Value: $8,646,401

Net Sale Proceeds

Calculates net proceeds from sale after selling costs and loan payoff.
• Terminal / Reversion Value: $8,646,401
• Selling Cost Rate: 2.0%
• Loan Payoff at Sale: $4,405,358
• Net Sale Proceeds: $4,068,115

Cumulative Distributions Including Sale Series

Builds a running total of operating cash flow over the hold and adds the net sale proceeds in the final year.
• Hold Period (Scalar Years): 5
• Projected NOI Series: See table above
• Annual Debt Service: $373,634
• Net Sale Proceeds: $4,068,115
• Cumulative Distributions Including Sale Series:
#Cumulative + Sale
1$111,166
2$236,876
3$377,567
4$533,687
5$4,773,814

Cumulative Return vs. Equity Invested Chart

Produces a year-by-year chart comparing cumulative distributions, including sale proceeds in the final year, against the equity invested. The year the bars overtake the line is the equity payback year; the final bar over the line shows the equity multiple.
Cumulative DistributionsEquity Invested
Requested result for Cumulative Return vs. Equity Invested Chart included above.
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Yield on cost, $12M value-add open ▾
TrueMath
Public Library ▾
···
Going-in NOI 980K on a $12M deal, stabilize to 1.2M…
▤ CRE Acquisitions Analyst simulation ╃ Scenarios↗ Share
Chat · Natural LanguageRequest
Going-in NOI is 980,000 on a 12,000,000 deal. I'll spend 600,000 to stabilize at 1,200,000 NOI, closing 1.5%. What's my yield on cost?
ENGINE INPUT (LANGUAGE MODEL INTERPRETATION)
noi: 980000 USD
property_value: 12000000 USD
initial_capex: 600000 USD
stabilized_noi: 1200000 USD
closing_cost_rate: 1.5%
calculate: yield_on_cost
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Jul 9, 2026 4:05 PMResponse
Creating Scenario 1.

Closing Costs

Calculates closing costs as a percentage of property value.
• Property Value / Purchase Price: $12,000,000
• Closing Cost Rate: 1.5%
• Closing Costs: $180,000

Total Basis

Calculates total cost basis as purchase price plus closing costs plus any immediate acquisition CapEx.
• Property Value / Purchase Price: $12,000,000
• Closing Costs: $180,000
• Initial Acquisition CapEx: $600,000
• Total Basis: $12,780,000

Yield on Cost

Calculates the unlevered yield on total invested cost at stabilization.
• Stabilized NOI: $1,200,000
• Total Basis: $12,780,000
• Yield on Cost: 9.39%
Requested result for Yield on Cost is 9.39%.
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02 The comparison

Watch how LLMs really work.

One prompt. Ten runs each. Nothing staged.
The prompt, sent to each“A 7,000,000 deal: NOI 450,000 growing 3%, 5-year hold, 65% LTV at 7% on 30-year am, closing 1.5%, exit cap 6.5%, selling costs 2%. What's my levered IRR?”
The exact answer · 5-year levered IRR
10.8463781499708%
● RAW LLM
0/10 exact
methods10 distinct
avg time29.7 s
energy / call~1.5 Wh
● TRUEMATH
10/10 exact
method1, auditable
avg time3.1 s9.6× faster
energy / call~0.003 Wh~500× less
Claude Opus 4.8 vs TrueMath via natural language, 10 runs each. Energy is inference-only; datacenter cooling widens the gap.
TrueMath was 9.6x faster, 500x more energy efficient, and delivered 10 identically precise answers using one fixed auditable method.
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