Cash-on-cash at the speed of conversation.
With receipts.

Ask in plain English. Get a number you can stand behind before you wire the earnest money.

01 The demo
Watch it run, right here. Tap a prompt, then hit Ask ↓
Duplex cash-on-cash, $320K, 25% down open ▾
TrueMath
Public Library ▾
···
I'm looking at a $320,000 duplex that rents for $3,500 a month…
▤ Real Estate Investor simulation ╃ Scenarios↗ Share
Chat · Natural LanguageRequest
I'm looking at a $320,000 duplex that rents for $3,500 a month. Figure 7% vacancy and operating expenses around 38% of rent. I'll put 25% down on a 30-year loan at 6.75%, with about $6,400 in closing costs. What's my cash-on-cash return?
ENGINE INPUT (LANGUAGE MODEL INTERPRETATION)
property_value: 320000 USD
gross_annual_rents: 42000 USD
vacancy_rate: 7%
expense_ratio: 38%
down_payment_pct: 25%
loan_term_years: 30 yr
interest_rate: 6.75%
closing_costs: 6400 USD
calculate: cash_on_cash_return
↑ This prompt is loaded and ready. Hit Ask to watch TrueMath work.
Jul 31, 2026 8:47 AMResponse
Creating Scenario 1.

Effective Gross Income

Gross annual rents adjusted for vacancy: rents times one minus the vacancy rate.
• Effective Gross Income: $39,060.00
• Gross Annual Rents: $42,000.00
• Vacancy Rate: 7.00%

Annual Operating Expenses

Operating expenses as a share of effective gross income; excludes debt service.
• Annual Operating Expenses: $14,842.80
• Effective Gross Income: $39,060.00
• Expense Ratio: 38.00%

Net Operating Income

Effective gross income minus operating expenses, before debt service.
• Net Operating Income: $24,217.20
• Effective Gross Income: $39,060.00
• Annual Operating Expenses: $14,842.80

Down Payment

Property value times the down payment percent.
• Down Payment: $80,000.00
• Property Value: $320,000.00
• Down Payment Percent: 25.00%

Loan Amount

Property value minus the down payment.
• Loan Amount: $240,000.00
• Property Value: $320,000.00
• Down Payment: $80,000.00

Monthly Debt Service

Fully amortizing principal and interest at the 6.750% rate over the 360-month term.
• Monthly PI Payment: $1,556.64
• Loan Amount: $240,000.00
• Interest Rate: 6.750%
• Loan Term (Months): 360

Annual Debt Service

Monthly principal and interest times twelve.
• Annual Debt Service: $18,679.63
• Monthly PI Payment: $1,556.64

Cash to Close

Total cash invested: down payment plus closing costs plus any renovation.
• Cash to Close: $86,400.00
• Down Payment: $80,000.00
• Closing Costs: $6,400.00
• Renovation Cost: $0.00

Annual Net Cash Flow

NOI minus annual debt service.
• Annual Net Cash Flow: $5,537.57
• Net Operating Income: $24,217.20
• Annual Debt Service: $18,679.63
Requested result for Cash-on-Cash Return is 6.41%.
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BRRRR post-refi cash-on-cash, $210K in open ▾
TrueMath
Public Library ▾
···
I'm $210,000 of my own cash into a BRRRR…
▤ Real Estate Investor simulation ╃ Scenarios↗ Share
Chat · Natural LanguageRequest
I'm $210,000 of my own cash into a BRRRR, all in with the purchase and rehab. It appraises at $260,000, and I'm doing a 75% cash-out refinance at 7.5% on a 30-year loan, with about $5,000 in refi costs. I paid cash, so there's no acquisition loan to pay off. Stabilized, it nets $24,000 a year. After I pull my cash back out at the refinance, what's my cash-on-cash return?
ENGINE INPUT (LANGUAGE MODEL INTERPRETATION)
cash_to_close: 210000 USD
after_repair_value: 260000 USD
refinance_ltv: 75%
refinance_interest_rate: 7.5%
refinance_loan_term_years: 30 yr
refinance_costs: 5000 USD
debt_retired_at_refi: 0 USD
noi: 24000 USD
calculate: post_refi_cash_on_cash
↑ This prompt is loaded and ready. Hit Ask to watch TrueMath work.
Jul 31, 2026 6:12 PMResponse
Creating Scenario 1.

Refinance Loan Amount

The cash-out refinance loan: after-repair value times the refinance LTV.
• Refinance Loan Amount: $195,000
• After-Repair Value: $260,000
• Refinance LTV: 75.00%

Refinance Monthly Debt Service

Fully amortizing principal and interest on the refinance loan at 7.500% over the 360-month term.
• Refinance Monthly PI: $1,363.47
• Refinance Loan Amount: $195,000
• Refinance Interest Rate: 7.500%
• Refinance Loan Term (Months): 360

Refinance Annual Debt Service

Refinance monthly payment times twelve.
• Refinance Annual Debt Service: $16,361.62
• Refinance Monthly PI: $1,363.47

Post-Refinance Annual Cash Flow

Stabilized NOI minus the refinance annual debt service.
• Post-Refinance Annual Cash Flow: $7,638.38
• Net Operating Income: $24,000.00
• Refinance Annual Debt Service: $16,361.62

Capital Recovered at Refinance

Cash pulled out at the refinance: the refinance loan minus debt retired minus refi costs.
• Capital Recovered: $190,000
• Refinance Loan Amount: $195,000
• Debt Retired at Refinance: $0
• Refinance Costs: $5,000.00

Capital Left in Deal

Total cash invested minus capital recovered — what's still tied up after the cash-out.
• Capital Left in Deal: $20,000
• Cash to Close: $210,000.00
• Capital Recovered: $190,000
Requested result for Post-Refinance Cash-on-Cash Return is 38.19%.
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Equity buildup, $320K duplex, 10-year hold open ▾
TrueMath
Public Library ▾
···
A $320,000 duplex with 25% down… show me how my equity grows…
▤ Real Estate Investor simulation ╃ Scenarios↗ Share
Chat · Natural LanguageRequest
A $320,000 duplex with 25% down on a 30-year loan at 6.75%. Assuming the property appreciates about 3% a year, show me how my equity grows over a 10-year hold.
ENGINE INPUT (LANGUAGE MODEL INTERPRETATION)
property_value: 320000 USD
down_payment_pct: 25%
loan_term_years: 30 yr
interest_rate: 6.75%
annual_appreciation_rate: 3%
hold_period_years: 10 yr
calculate: equity_series
↑ This prompt is loaded and ready. Hit Ask to watch TrueMath work.
Jul 31, 2026 11:24 AMResponse
Creating Scenario 1.

Loan Amount

Property value minus the 25% down payment.
• Loan Amount: $240,000.00
• Property Value: $320,000.00
• Down Payment: $80,000.00

Monthly Debt Service

Fully amortizing principal and interest at the 6.750% rate over the 360-month term.
• Monthly PI Payment: $1,556.64
• Loan Amount: $240,000.00
• Interest Rate: 6.750%
• Loan Term (Months): 360

Equity Buildup Over the Hold

Year-by-year equity: appreciated value minus the remaining loan balance. Appreciation lifts the value while amortization pays the balance down, so equity compounds from both.
Equity

Equity by Year

The full year-by-year equity position over the 10-year hold.
#Equity
1$92,158
2$104,782
3$117,893
4$131,513
5$145,666
6$160,376
7$175,670
8$191,574
9$208,117
10$225,331
• Appreciated value, year 10: $430,053
• Loan balance, year 10: $204,722
Requested result for Equity Series: equity grows from $92,158 in year 1 to $225,331 by year 10.
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Real TrueMath output, replayed here. Open a prompt, hit Ask, watch the work.
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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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