io.github.VladimirWrites/nestegg-calculators

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Les 99 outils

• accrued-interest≈ 216 tokens

  Accrued interest since the last coupon: the annual coupon pro-rated by days elapsed over the day-count basis.

  Paramètres, retour & exemple (4)

  Paramètres

  • faceValue · number · requis
    Face value.
  • couponRatePct · number · requis
    Annual coupon rate in percent.
  • dayCountBasis · number · optionnel
    Day-count basis (default 360).
  • daysSinceLastCoupon · number · requis
    Days since the last coupon.

  Exemple d'appel

  {"name": "accrued-interest", "arguments": {"faceValue": 1, "couponRatePct": 1, "daysSinceLastCoupon": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"accrued": 1}}

• after-tax-yield≈ 158 tokens

  After-tax yield: a yield reduced by the tax rate. Percents in and out.

  Paramètres, retour & exemple (2)

  Paramètres

  • yieldPct · number · requis
    Pre-tax yield in percent.
  • taxRatePct · number · requis
    Tax rate in percent.

  Exemple d'appel

  {"name": "after-tax-yield", "arguments": {"yieldPct": 1, "taxRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"afterTaxPct": 1}}

• amortization≈ 844 tokens

  Monthly loan amortization schedule and summary. Supports dated extra principal payments and a rate-fixed period. detail controls output size: 'summary' (default) returns totals plus a per-year breakdown; 'monthly' returns the full schedule (paginate with offset/limit). Returns numbers and schedules; no advice.

  Paramètres, retour & exemple (12)

  Paramètres

  • mode · string · requis · term | payment
    Fix the term (compute the payment) or fix the payment (compute the term).
  • rate · number · requis
    Annual interest rate in percent (6 = 6%).
  • extra · array · optionnel
    Optional dated extra principal payments.
  • limit · number · optionnel
    Max monthly rows when detail=monthly (default and maximum 360; page with nextOffset).
  • amount · number · requis
    Loan principal.
  • detail · string · optionnel · summary | yearly | monthly
    Output size. summary (default): totals + yearly breakdown. monthly: full schedule (use offset/limit to paginate).
  • offset · number · optionnel
    Monthly schedule start index when detail=monthly (default 0).
  • payment · number · optionnel
    Monthly payment, used when mode is 'payment'.
  • rateSteps · array · optionnel
    Optional rate changes (e.g. after a Zinsbindung). The installment is held; from each date the outstanding balance continues at the new annual rate.
  • startDate · string · requis
    First payment month as an ISO date (YYYY-MM-DD).
  • termYears · number · optionnel
    Term in years, used when mode is 'term'.
  • fixedUntil · string · optionnel
    Optional. Rate is certain until this ISO date; beyond it the schedule is an estimate.

  Exemple d'appel

  {"name": "amortization", "arguments": {"mode": "term", "rate": 1, "amount": 1, "startDate": "texte"}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"yearly": [], "payments": 1, "schedule": [], "totalPaid": 1, "nextOffset": 1, "payoffDate": "texte", "scheduleTotal": 1, "totalInterest": 1, "monthlyPayment": 1, "scheduledMonths": 1}}

• annuity-fv≈ 172 tokens

  Future value of an ordinary annuity. rate is the per-period rate in percent.

  Paramètres, retour & exemple (3)

  Paramètres

  • payment · number · requis
    Payment per period.
  • periods · number · requis
    Number of periods.
  • ratePct · number · requis
    Rate per period in percent.

  Exemple d'appel

  {"name": "annuity-fv", "arguments": {"payment": 1, "periods": 1, "ratePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"fv": 1}}

• annuity-payment≈ 192 tokens

  The level payment that amortizes a present value over n periods (the loan-payment formula). rate is per period.

  Paramètres, retour & exemple (3)

  Paramètres

  • periods · number · requis
    Number of periods.
  • ratePct · number · requis
    Rate per period in percent.
  • presentValue · number · requis
    Present value / principal.

  Exemple d'appel

  {"name": "annuity-payment", "arguments": {"periods": 1, "ratePct": 1, "presentValue": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"payment": 1}}

• annuity-pv≈ 182 tokens

  Present value of an ordinary annuity (level payment at each period end). rate is the per-period rate in percent.

  Paramètres, retour & exemple (3)

  Paramètres

  • payment · number · requis
    Payment per period.
  • periods · number · requis
    Number of periods.
  • ratePct · number · requis
    Rate per period in percent.

  Exemple d'appel

  {"name": "annuity-pv", "arguments": {"payment": 1, "periods": 1, "ratePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"pv": 1}}

• balloon-loan≈ 231 tokens

  Balloon loan: payment based on a long amortization, with the balloon being the balance still due after the shorter balloon term.

  Paramètres, retour & exemple (4)

  Paramètres

  • amount · number · requis
    Loan amount.
  • ratePct · number · requis
    Annual rate in percent.
  • amortMonths · number · requis
    Amortization basis in months.
  • balloonMonths · number · requis
    Months until the balloon is due.

  Exemple d'appel

  {"name": "balloon-loan", "arguments": {"amount": 1, "ratePct": 1, "amortMonths": 1, "balloonMonths": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"balloon": 1, "payment": 1}}

• barista-fire≈ 210 tokens

  Barista FIRE: the nest egg needed when part-time income covers part of the spending, so the portfolio only funds the remainder at the safe withdrawal rate.

  Paramètres, retour & exemple (3)

  Paramètres

  • annualSpend · number · requis
    Yearly spending.
  • partTimeIncome · number · requis
    Yearly part-time income.
  • withdrawalRatePct · number · optionnel
    Safe withdrawal rate in percent (default 4).

  Exemple d'appel

  {"name": "barista-fire", "arguments": {"annualSpend": 1, "partTimeIncome": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"target": 1}}

• biweekly-payoff≈ 228 tokens

  Biweekly mortgage acceleration: paying half the monthly payment every two weeks. Returns the biweekly payment and the months and interest saved.

  Paramètres, retour & exemple (3)

  Paramètres

  • amount · number · requis
    Loan amount.
  • ratePct · number · requis
    Annual rate in percent.
  • termMonths · number · requis
    Original term in months.

  Exemple d'appel

  {"name": "biweekly-payoff", "arguments": {"amount": 1, "ratePct": 1, "termMonths": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"monthsSaved": 1, "interestSaved": 1, "biweeklyPayment": 1}}

• black-scholes≈ 318 tokens

  Black-Scholes price of a European call or put option, plus d1/d2. Volatility and rates in percent; optional continuous dividend yield.

  Paramètres, retour & exemple (7)

  Paramètres

  • spot · number · requis
    Current underlying price.
  • type · string · optionnel · call | put
    Option type (default call).
  • years · number · requis
    Time to expiry in years.
  • strike · number · requis
    Strike price.
  • riskFreePct · number · requis
    Risk-free rate in percent.
  • volatilityPct · number · requis
    Annualized volatility in percent.
  • dividendYieldPct · number · optionnel
    Continuous dividend yield in percent (default 0).

  Exemple d'appel

  {"name": "black-scholes", "arguments": {"spot": 1, "years": 1, "strike": 1, "riskFreePct": 1, "volatilityPct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"d1": 1, "d2": 1, "price": 1}}

• bond-duration≈ 251 tokens

  Macaulay duration (PV-weighted average time of cashflows, in years) and modified duration (price sensitivity to yield).

  Paramètres, retour & exemple (5)

  Paramètres

  • years · number · requis
    Years to maturity.
  • yieldPct · number · requis
    Annual yield in percent.
  • faceValue · number · requis
    Face value.
  • couponRatePct · number · requis
    Annual coupon rate in percent.
  • periodsPerYear · number · optionnel
    Coupon periods per year (default 2).

  Exemple d'appel

  {"name": "bond-duration", "arguments": {"years": 1, "yieldPct": 1, "faceValue": 1, "couponRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"macaulay": 1, "modified": 1}}

• bond-price≈ 230 tokens

  Price of a coupon bond given a yield: present value of the coupons plus the face at maturity.

  Paramètres, retour & exemple (5)

  Paramètres

  • years · number · requis
    Years to maturity.
  • yieldPct · number · requis
    Annual yield in percent.
  • faceValue · number · requis
    Face (par) value.
  • couponRatePct · number · requis
    Annual coupon rate in percent of face.
  • periodsPerYear · number · optionnel
    Coupon periods per year (default 2).

  Exemple d'appel

  {"name": "bond-price", "arguments": {"years": 1, "yieldPct": 1, "faceValue": 1, "couponRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"price": 1}}

• break-even-units≈ 225 tokens

  Break-even volume: fixed costs divided by the per-unit contribution (price - variable cost), plus the revenue at that volume.

  Paramètres, retour & exemple (3)

  Paramètres

  • fixedCosts · number · requis
    Total fixed costs.
  • pricePerUnit · number · requis
    Selling price per unit.
  • variableCostPerUnit · number · requis
    Variable cost per unit.

  Exemple d'appel

  {"name": "break-even-units", "arguments": {"fixedCosts": 1, "pricePerUnit": 1, "variableCostPerUnit": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"units": 1, "revenue": 1}}

• budget-50-30-20≈ 166 tokens

  The 50/30/20 budget split of monthly income into needs, wants, and savings.

  Paramètres, retour & exemple (1)

  Paramètres

  • monthlyIncome · number · requis
    Monthly take-home income.

  Exemple d'appel

  {"name": "budget-50-30-20", "arguments": {"monthlyIncome": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"needs": 1, "wants": 1, "savings": 1}}

• cagr≈ 166 tokens

  Compound annual growth rate between two values over a number of years. Returns a decimal (0.07 means 7%).

  Paramètres, retour & exemple (3)

  Paramètres

  • end · number · requis
    Ending value.
  • begin · number · requis
    Starting value.
  • years · number · requis
    Number of years.

  Exemple d'appel

  {"name": "cagr", "arguments": {"end": 1, "begin": 1, "years": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"value": 1}}

• cap-rate≈ 155 tokens

  Capitalization rate: net operating income as a percent of property value.

  Paramètres, retour & exemple (2)

  Paramètres

  • noi · number · requis
    Net operating income.
  • propertyValue · number · requis
    Property value.

  Exemple d'appel

  {"name": "cap-rate", "arguments": {"noi": 1, "propertyValue": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"capRatePct": 1}}

• cash-on-cash≈ 170 tokens

  Cash-on-cash return: annual pre-tax cash flow as a percent of the cash invested.

  Paramètres, retour & exemple (2)

  Paramètres

  • cashInvested · number · requis
    Cash invested.
  • annualCashFlow · number · requis
    Annual pre-tax cash flow.

  Exemple d'appel

  {"name": "cash-on-cash", "arguments": {"cashInvested": 1, "annualCashFlow": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"cashOnCashPct": 1}}

• coast-fire≈ 328 tokens

  Coast FIRE: whether the current nest egg, left to grow untouched to retirement, already reaches the FIRE target. Returns the target, the projected balance, whether it coasts, and any shortfall.

  Paramètres, retour & exemple (5)

  Paramètres

  • annualSpend · number · requis
    Yearly spending in retirement.
  • annualRatePct · number · requis
    Expected annual growth in percent.
  • currentNestEgg · number · requis
    Amount invested today.
  • withdrawalRatePct · number · optionnel
    Safe withdrawal rate in percent (default 4).
  • yearsToRetirement · number · requis
    Years until retirement.

  Exemple d'appel

  {"name": "coast-fire", "arguments": {"annualSpend": 1, "annualRatePct": 1, "currentNestEgg": 1, "yearsToRetirement": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"gap": 1, "projected": 1, "fireTarget": 1, "isCoasting": true}}

• compound-interest≈ 255 tokens

  Compound growth at any frequency, with an optional contribution each period (paid at period end). Generalizes future-value (periodsPerYear 1) and contributions (periodsPerYear 12).

  Paramètres, retour & exemple (5)

  Paramètres

  • years · number · requis
    Number of years.
  • principal · number · requis
    Starting amount.
  • annualRatePct · number · requis
    Annual growth rate in percent.
  • periodsPerYear · number · optionnel
    Compounding periods per year (default 1).
  • contributionPerPeriod · number · optionnel
    Optional. Amount added each period (default 0).

  Exemple d'appel

  {"name": "compound-interest", "arguments": {"years": 1, "principal": 1, "annualRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"value": 1}}

• contribution-margin≈ 190 tokens

  Contribution margin per unit and as a percent of price.

  Paramètres, retour & exemple (2)

  Paramètres

  • pricePerUnit · number · requis
    Selling price per unit.
  • variableCostPerUnit · number · requis
    Variable cost per unit.

  Exemple d'appel

  {"name": "contribution-margin", "arguments": {"pricePerUnit": 1, "variableCostPerUnit": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"ratioPct": 1, "contributionMargin": 1}}

• contributions≈ 207 tokens

  Future value of a fixed monthly contribution, optionally stepping up each year.

  Paramètres, retour & exemple (4)

  Paramètres

  • months · number · requis
    Number of months.
  • monthly · number · requis
    Monthly contribution.
  • annualRatePct · number · requis
    Annual growth rate in percent.
  • contribGrowthPct · number · optionnel
    Optional. Contribution step-up percent per year.

  Exemple d'appel

  {"name": "contributions", "arguments": {"months": 1, "monthly": 1, "annualRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"value": 1}}

• convexity≈ 226 tokens

  Bond convexity (years^2): the curvature of price with respect to yield, used alongside duration.

  Paramètres, retour & exemple (5)

  Paramètres

  • years · number · requis
    Years to maturity.
  • yieldPct · number · requis
    Annual yield in percent.
  • faceValue · number · requis
    Face value.
  • couponRatePct · number · requis
    Annual coupon rate in percent.
  • periodsPerYear · number · optionnel
    Coupon periods per year (default 2).

  Exemple d'appel

  {"name": "convexity", "arguments": {"years": 1, "yieldPct": 1, "faceValue": 1, "couponRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"convexity": 1}}

• credit-card-payoff≈ 244 tokens

  Months to clear a credit-card balance at a fixed monthly payment, plus interest paid. Null when the payment can't cover the first month's interest.

  Paramètres, retour & exemple (3)

  Paramètres

  • aprPct · number · requis
    Annual percentage rate in percent.
  • balance · number · requis
    Current balance.
  • monthlyPayment · number · requis
    Fixed monthly payment.

  Exemple d'appel

  {"name": "credit-card-payoff", "arguments": {"aprPct": 1, "balance": 1, "monthlyPayment": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"months": 1, "totalPaid": 1, "totalInterest": 1}}

• current-ratio≈ 161 tokens

  Current ratio: current assets over current liabilities.

  Paramètres, retour & exemple (2)

  Paramètres

  • currentAssets · number · requis
    Current assets.
  • currentLiabilities · number · requis
    Current liabilities.

  Exemple d'appel

  {"name": "current-ratio", "arguments": {"currentAssets": 1, "currentLiabilities": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"currentRatio": 1}}

• current-yield≈ 186 tokens

  Current yield: the annual coupon as a percent of the bond's current price.

  Paramètres, retour & exemple (3)

  Paramètres

  • price · number · requis
    Current bond price.
  • faceValue · number · requis
    Face value.
  • couponRatePct · number · requis
    Annual coupon rate in percent of face.

  Exemple d'appel

  {"name": "current-yield", "arguments": {"price": 1, "faceValue": 1, "couponRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"currentYieldPct": 1}}

• de-abgeltungsteuer≈ 478 tokens

  German flat tax on capital income (Abgeltungsteuer, §32d EStG) for tax years 2023-2026 with the year's Sparerpauschbetrag built in. 25% above the allowance, Soli 5.5% on top (no Freigrenze for capital income), and with church tax the statutory reduced rate (e.g. 24.45% at 9%) plus the church tax itself.

  Paramètres, retour & exemple (5)

  Paramètres

  • year · number · requis
    Tax year: 2023, 2024, 2025 or 2026.
  • joint · boolean · optionnel
    true for jointly assessed couples (doubles the Sparerpauschbetrag).
  • churchTaxPct · number · optionnel
    Church tax rate: 8, 9, or 0 for none (default 0).
  • capitalIncome · number · requis
    Annual capital income (interest, dividends, realized gains) in EUR.
  • foreignTaxCredit · number · optionnel
    Optional. Creditable foreign withholding tax (q in the §32d formula).

  Exemple d'appel

  {"name": "de-abgeltungsteuer", "arguments": {"year": 1, "capitalIncome": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"net": 1, "soli": 1, "year": 1, "taxable": 1, "totalTax": 1, "allowance": 1, "churchTax": 1, "incomeTax": 1, "capitalIncome": 1, "effectiveRatePct": 1}}

• de-gross-to-net≈ 584 tokens

  German net (Netto) salary from gross (Brutto). No tax tables are baked in: look up the current year's statutory figures and pass them in. Income tax (Lohnsteuer) and Soli are amounts; church tax is a percent of the income tax; the four employee social rates and the two contribution ceilings are inputs. Use consistent units (e.g. all annual).

  Paramètres, retour & exemple (10)

  Paramètres

  • soli · number · optionnel
    Solidarity surcharge (Solidaritätszuschlag) amount (often 0 below the threshold).
  • gross · number · requis
    Gross salary (Brutto).
  • carePct · number · optionnel
    Employee long-term care (Pflegeversicherung) rate in percent.
  • healthPct · number · optionnel
    Employee health (Krankenversicherung incl. Zusatzbeitrag) rate in percent.
  • incomeTax · number · optionnel
    Income tax (Lohnsteuer) amount for the period — look up via the §32a / Steuerklasse tables.
  • pensionPct · number · optionnel
    Employee pension (Rentenversicherung) rate in percent (e.g. 9.3).
  • churchTaxPct · number · optionnel
    Church tax (Kirchensteuer) rate in percent of income tax (8 or 9, 0 if none).
  • healthCeiling · number · optionnel
    Contribution ceiling for health and care.
  • pensionCeiling · number · optionnel
    Contribution ceiling (Beitragsbemessungsgrenze) for pension and unemployment.
  • unemploymentPct · number · optionnel
    Employee unemployment (Arbeitslosenversicherung) rate in percent (e.g. 1.3).

  Exemple d'appel

  {"name": "de-gross-to-net", "arguments": {"gross": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"net": 1, "soli": 1, "gross": 1, "churchTax": 1, "incomeTax": 1, "contributions": {}, "totalDeductions": 1}}

• de-kindergeld≈ 239 tokens

  German child benefit (Kindergeld) for 2023-2026: the year's flat monthly amount per child (uniform since 2023), as monthly and annual totals.

  Paramètres, retour & exemple (2)

  Paramètres

  • year · number · requis
    Year: 2023, 2024, 2025 or 2026.
  • children · number · optionnel
    Number of children (default 1).

  Exemple d'appel

  {"name": "de-kindergeld", "arguments": {"year": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"year": 1, "annual": 1, "monthly": 1, "children": 1, "perChildMonthly": 1}}

• de-midijob≈ 542 tokens

  German Midijob / Uebergangsbereich (paragraph 20 Abs. 2a SGB IV) for 2023-2026: classifies a monthly pay as Minijob / Midijob / regular against the year's thresholds and, inside the Midijob band, computes the reduced contribution bases (Faktor F from the year's rates) and the employee vs employer social-insurance split.

  Paramètres, retour & exemple (7)

  Paramètres

  • age · number · optionnel
    Optional. Age - under 23 skips the childless care surcharge.
  • year · number · requis
    Year: 2023, 2024, 2025 or 2026.
  • children · number · optionnel
    Children, for the care-insurance rate (default 0).
  • bundesland · string · optionnel
    Optional. State code; SN applies the Saxony care split.
  • monthlyPay · number · requis
    Gross monthly pay in EUR.
  • kvZusatzPct · number · optionnel
    Optional. Krankenkasse Zusatzbeitrag in percent; defaults to the year's average.
  • childrenUnder25 · number · optionnel
    Optional. Children under 25 for the care discounts, when different.

  Exemple d'appel

  {"name": "de-midijob", "arguments": {"year": 1, "monthlyPay": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"year": 1, "zone": "texte", "rates": {}, "faktorF": 1, "employee": {}, "employer": {}, "monthlyPay": 1, "thresholds": {}, "savingsVsFull": 1, "contributionBase": {}}}

• de-net-salary≈ 851 tokens

  Exact German net (Netto) salary from annual gross (Brutto) for tax years 2023-2026. Income tax and Soli follow the official BMF Programmablaufplan for the year (to the euro; 2024 uses the retroactive December tariff), church tax comes from the PAP's Kirchensteuer base, and employee social insurance uses that year's ceilings and rates (KV Zusatzbeitrag defaults to the year's average). Earlier years are rejected - use de-gross-to-net with self-supplied figures instead.

  Paramètres, retour & exemple (11)

  Paramètres

  • age · number · optionnel
    Optional. Age in years - under 23 skips the childless care surcharge.
  • year · number · requis
    Tax year: 2023, 2024, 2025 or 2026.
  • faktor · number · optionnel
    Optional. Tax-class-4 Faktorverfahren factor, default 1.0 (no factor). Only the small minority of married IV/IV couples who applied for it have one; it is assigned by the Finanzamt and printed on the payslip / ELStAM (e.g. 0.921, always <= 1). Leave unset unless the payslip shows a Faktor.
  • children · number · optionnel
    Kinderfreibetrag counter (ZKF), halves allowed (default 0). Also drives the care-insurance child discounts.
  • taxClass · number · optionnel
    Steuerklasse 1-6 (default 1).
  • bundesland · string · optionnel
    Optional. State code (BW, BY, BE, ... SN, TH). Drives the Saxony care-insurance split and the pre-2025 East pension ceiling.
  • grossAnnual · number · requis
    Annual gross salary (Brutto) in EUR.
  • kvZusatzPct · number · optionnel
    Optional. The Krankenkasse's own Zusatzbeitrag in percent — pass the actual rate for exact results (rates change yearly, e.g. TK 2025: 2.45, 2026: 2.69). Defaults to the year's official average, which is only right for generic estimates.
  • churchTaxPct · number · optionnel
    Church tax rate: 8, 9, or 0 for none (default 0).
  • privateHealth · object · optionnel
  • childrenUnder25 · number · optionnel
    Optional. Children under 25 for the care-insurance discounts, when it differs from `children`.

  Exemple d'appel

  {"name": "de-net-salary", "arguments": {"year": 1, "grossAnnual": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"net": {}, "soli": 1, "year": 1, "gross": {}, "totalTax": 1, "churchTax": 1, "incomeTax": 1, "assumptions": {}, "contributions": {}, "totalDeductions": 1}}

• de-rentenpunkte≈ 474 tokens

  German pension points (Entgeltpunkte, paragraph 63 SGB VI) for 2023-2026: points earned from an annual gross via the year's Durchschnittsentgelt (capped at the contribution ceiling), the aktueller Rentenwert for both halves of the year, and optionally the gross monthly state pension for a total point count.

  Paramètres, retour & exemple (4)

  Paramètres

  • year · number · requis
    Year: 2023, 2024, 2025 or 2026.
  • bundesland · string · optionnel
    Optional. State code - East states use the East ceiling before 2025.
  • grossAnnual · number · requis
    Annual insured gross salary in EUR.
  • totalPoints · number · optionnel
    Optional. Accumulated points, to project the gross monthly pension at today's Rentenwert.

  Exemple d'appel

  {"name": "de-rentenpunkte", "arguments": {"year": 1, "grossAnnual": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"year": 1, "points": 1, "projection": {}, "rentenwert": {}, "grossAnnual": 1, "insuredGross": 1, "ceilingApplied": true, "maxPointsThisYear": 1, "durchschnittsentgelt": 1, "monthlyPensionPerPoint": 1}}

• debt-payoff≈ 398 tokens

  Multi-debt payoff plan under a fixed monthly budget. method 'avalanche' (highest rate first) minimizes interest; 'snowball' (smallest balance first) clears accounts soonest. Returns months, total interest, and payoff order; flags insolvent budgets.

  Paramètres, retour & exemple (3)

  Paramètres

  • debts · array · requis
    The debts to pay off.
  • method · string · optionnel · avalanche | snowball
    Payoff strategy (default avalanche).
  • monthlyBudget · number · requis
    Total amount available across all debts each month.

  Exemple d'appel

  {"name": "debt-payoff", "arguments": {"debts": [], "monthlyBudget": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"months": 1, "insolvent": true, "payoffOrder": [], "totalInterest": 1}}

• declining-balance-depreciation≈ 221 tokens

  Declining-balance depreciation: a fixed percent of the reducing book value, for a given year. Returns that year's depreciation and the remaining book value.

  Paramètres, retour & exemple (3)

  Paramètres

  • year · number · requis
    Year (1-based).
  • value · number · requis
    Initial cost.
  • ratePct · number · requis
    Annual depreciation rate in percent.

  Exemple d'appel

  {"name": "declining-balance-depreciation", "arguments": {"year": 1, "value": 1, "ratePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"bookValue": 1, "depreciation": 1}}

• depreciate≈ 207 tokens

  Value after compounding down (or up) at a yearly percentage rate over a number of years. This is the method the app uses for long-term assets.

  Paramètres, retour & exemple (4)

  Paramètres

  • up · boolean · optionnel
    false depreciates, true appreciates.
  • value · number · requis
    Starting value.
  • years · number · requis
    Number of years.
  • annualRatePct · number · requis
    Annual rate in percent.

  Exemple d'appel

  {"name": "depreciate", "arguments": {"value": 1, "years": 1, "annualRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"value": 1}}

• discount≈ 162 tokens

  A single percentage discount: the amount off and the final price.

  Paramètres, retour & exemple (2)

  Paramètres

  • price · number · requis
    Original price.
  • discountPct · number · requis
    Discount in percent.

  Exemple d'appel

  {"name": "discount", "arguments": {"price": 1, "discountPct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"discount": 1, "finalPrice": 1}}

• discounted-payback≈ 200 tokens

  Discounted payback period: like payback-period but each cashflow is discounted at the per-period rate.

  Paramètres, retour & exemple (3)

  Paramètres

  • ratePct · number · requis
    Discount rate per period in percent.
  • cashflows · array · requis
    Inflow each period.
  • initialCost · number · requis
    Upfront cost.

  Exemple d'appel

  {"name": "discounted-payback", "arguments": {"ratePct": 1, "cashflows": [], "initialCost": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"years": 1}}

• dollar-cost-averaging≈ 255 tokens

  Dollar-cost averaging: buying a fixed amount each period at the given prices. Returns units accumulated, total invested, average cost, and final value at the last price.

  Paramètres, retour & exemple (2)

  Paramètres

  • prices · array · requis
    Price at each purchase period.
  • periodicInvestment · number · requis
    Fixed amount invested each period.

  Exemple d'appel

  {"name": "dollar-cost-averaging", "arguments": {"prices": [], "periodicInvestment": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"units": 1, "avgCost": 1, "invested": 1, "finalValue": 1}}

• double-declining-depreciation≈ 226 tokens

  Double-declining-balance depreciation: 2/usefulYears of the book value each year, not falling below salvage.

  Paramètres, retour & exemple (4)

  Paramètres

  • year · number · requis
    Year (1-based).
  • value · number · requis
    Initial cost.
  • salvage · number · optionnel
    Salvage value (default 0).
  • usefulYears · number · requis
    Useful life in years.

  Exemple d'appel

  {"name": "double-declining-depreciation", "arguments": {"year": 1, "value": 1, "usefulYears": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"bookValue": 1, "depreciation": 1}}

• dscr≈ 165 tokens

  Debt service coverage ratio: net operating income divided by annual debt service.

  Paramètres, retour & exemple (2)

  Paramètres

  • noi · number · requis
    Net operating income.
  • annualDebtService · number · requis
    Annual debt service.

  Exemple d'appel

  {"name": "dscr", "arguments": {"noi": 1, "annualDebtService": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"dscr": 1}}

• dti≈ 164 tokens

  Debt-to-income ratio, percent (monthly debt / gross monthly income).

  Paramètres, retour & exemple (2)

  Paramètres

  • monthlyDebt · number · requis
    Total monthly debt payments.
  • grossMonthlyIncome · number · requis
    Gross monthly income.

  Exemple d'appel

  {"name": "dti", "arguments": {"monthlyDebt": 1, "grossMonthlyIncome": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"dtiPct": 1}}

• effective-rate≈ 258 tokens

  Convert a nominal annual rate to the effective annual rate (APY) for a compounding frequency, or with toNominal recover the nominal rate from an APY.

  Paramètres, retour & exemple (3)

  Paramètres

  • ratePct · number · requis
    The rate in percent (nominal, or effective when toNominal is true).
  • toNominal · boolean · optionnel
    false (default) returns the effective rate; true returns the nominal rate.
  • periodsPerYear · number · requis
    Compounding periods per year (12 monthly, 365 daily).

  Exemple d'appel

  {"name": "effective-rate", "arguments": {"ratePct": 1, "periodsPerYear": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"nominalRatePct": 1, "effectiveRatePct": 1}}

• emergency-fund≈ 165 tokens

  Months of runway: liquid savings divided by monthly expenses.

  Paramètres, retour & exemple (2)

  Paramètres

  • liquidSavings · number · requis
    Cash and liquid savings on hand.
  • monthlyExpenses · number · requis
    Total monthly expenses.

  Exemple d'appel

  {"name": "emergency-fund", "arguments": {"liquidSavings": 1, "monthlyExpenses": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"months": 1}}

• fee-drag≈ 236 tokens

  Effect of an annual fee: the compounded balance at the gross rate vs net of the fee, and the amount lost to fees.

  Paramètres, retour & exemple (4)

  Paramètres

  • years · number · requis
    Number of years.
  • feePct · number · requis
    Annual fee in percent.
  • principal · number · requis
    Starting amount.
  • grossAnnualPct · number · requis
    Gross annual return in percent.

  Exemple d'appel

  {"name": "fee-drag", "arguments": {"years": 1, "feePct": 1, "principal": 1, "grossAnnualPct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"net": 1, "gross": 1, "lostToFees": 1}}

• fire-number≈ 308 tokens

  FIRE target nest egg from annual spend and a safe withdrawal rate (default 4%), plus the gap from today and the years to reach it given optional savings and growth. No advice.

  Paramètres, retour & exemple (5)

  Paramètres

  • annualSpend · number · requis
    Yearly spending the nest egg must cover.
  • annualRatePct · number · optionnel
    Optional. Annual portfolio growth in percent (default 0).
  • currentNestEgg · number · optionnel
    Optional. Amount already saved (default 0).
  • withdrawalRatePct · number · optionnel
    Safe withdrawal rate in percent (default 4 = the 4% rule).
  • annualContribution · number · optionnel
    Optional. Amount saved per year (default 0).

  Exemple d'appel

  {"name": "fire-number", "arguments": {"annualSpend": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"gap": 1, "target": 1, "yearsToFI": 1}}

• future-value≈ 169 tokens

  Future value of a single lump sum compounded annually.

  Paramètres, retour & exemple (3)

  Paramètres

  • years · number · requis
    Number of years.
  • principal · number · requis
    Starting amount.
  • annualRatePct · number · requis
    Annual growth rate in percent.

  Exemple d'appel

  {"name": "future-value", "arguments": {"years": 1, "principal": 1, "annualRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"value": 1}}

• fx-convert≈ 164 tokens

  Convert an amount using a rate supplied by the caller (units of target currency per unit of source). No rate is ever looked up.

  Paramètres, retour & exemple (2)

  Paramètres

  • rate · number · requis
    Rate: target units per source unit.
  • amount · number · requis
    Amount to convert.

  Exemple d'appel

  {"name": "fx-convert", "arguments": {"rate": 1, "amount": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"value": 1}}

• gross-rent-multiplier≈ 158 tokens

  Gross rent multiplier: price divided by gross annual rent.

  Paramètres, retour & exemple (2)

  Paramètres

  • price · number · requis
    Purchase price.
  • grossAnnualRent · number · requis
    Gross annual rent.

  Exemple d'appel

  {"name": "gross-rent-multiplier", "arguments": {"price": 1, "grossAnnualRent": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"grm": 1}}

• holding-period-return≈ 186 tokens

  Holding-period return: (income + capital gain) / starting value, in percent.

  Paramètres, retour & exemple (3)

  Paramètres

  • income · number · requis
    Income received over the period.
  • endValue · number · requis
    Ending value.
  • beginValue · number · requis
    Starting value.

  Exemple d'appel

  {"name": "holding-period-return", "arguments": {"income": 1, "endValue": 1, "beginValue": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"hprPct": 1}}

• hourly-to-salary≈ 186 tokens

  Annualize an hourly rate (and the monthly equivalent).

  Paramètres, retour & exemple (3)

  Paramètres

  • hourlyRate · number · requis
    Hourly rate.
  • hoursPerWeek · number · optionnel
    Hours per week (default 40).
  • weeksPerYear · number · optionnel
    Weeks per year (default 52).

  Exemple d'appel

  {"name": "hourly-to-salary", "arguments": {"hourlyRate": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"annual": 1, "monthly": 1}}

• inflation-adjust≈ 225 tokens

  Convert a nominal amount to today's purchasing power (real), or with toNominal inflate a real amount forward, at a given annual inflation rate.

  Paramètres, retour & exemple (4)

  Paramètres

  • years · number · requis
    Number of years.
  • amount · number · requis
    Amount to adjust.
  • toNominal · boolean · optionnel
    false (default) deflates nominal to real; true inflates real to nominal.
  • inflationRatePct · number · requis
    Annual inflation rate in percent.

  Exemple d'appel

  {"name": "inflation-adjust", "arguments": {"years": 1, "amount": 1, "inflationRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"value": 1}}

• interest-only-payment≈ 150 tokens

  Interest-only monthly payment on a balance.

  Paramètres, retour & exemple (2)

  Paramètres

  • amount · number · requis
    Outstanding balance.
  • ratePct · number · requis
    Annual rate in percent.

  Exemple d'appel

  {"name": "interest-only-payment", "arguments": {"amount": 1, "ratePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"payment": 1}}

• intrinsic-time-value≈ 213 tokens

  Split an option premium into intrinsic value (in-the-money amount) and time value.

  Paramètres, retour & exemple (4)

  Paramètres

  • spot · number · requis
    Underlying price.
  • type · string · optionnel · call | put
    Option type (default call).
  • strike · number · requis
    Strike price.
  • premium · number · requis
    Option premium.

  Exemple d'appel

  {"name": "intrinsic-time-value", "arguments": {"spot": 1, "strike": 1, "premium": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"intrinsic": 1, "timeValue": 1}}

• irr≈ 172 tokens

  Internal rate of return: the per-period rate that zeroes the NPV of a cashflow series. Returns a percent, or null when the series never crosses zero.

  Paramètres, retour & exemple (1)

  Paramètres

  • cashflows · array · requis
    Cashflows by period, starting at period 0. Outflows are negative.

  Exemple d'appel

  {"name": "irr", "arguments": {"cashflows": []}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"irrPct": 1}}

• loan-apr≈ 217 tokens

  Effective APR including upfront fees: the note-rate payment priced against the net proceeds (amount - fees). Annual percent.

  Paramètres, retour & exemple (4)

  Paramètres

  • fees · number · optionnel
    Optional. Upfront fees / points in currency (default 0).
  • amount · number · requis
    Loan amount.
  • ratePct · number · requis
    Note (nominal) annual rate in percent.
  • termMonths · number · requis
    Term in months.

  Exemple d'appel

  {"name": "loan-apr", "arguments": {"amount": 1, "ratePct": 1, "termMonths": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"aprPct": 1}}

• loan-payoff≈ 467 tokens

  Time and interest saved by paying a fixed extra amount every month on a loan, versus the baseline schedule.

  Paramètres, retour & exemple (9)

  Paramètres

  • mode · string · requis · term | payment
    Fix the term (compute the payment) or fix the payment (compute the term).
  • rate · number · requis
    Annual interest rate in percent (6 = 6%).
  • extra · array · optionnel
    Optional dated extra principal payments.
  • amount · number · requis
    Loan principal.
  • payment · number · optionnel
    Monthly payment, used when mode is 'payment'.
  • startDate · string · requis
    First payment month as an ISO date (YYYY-MM-DD).
  • termYears · number · optionnel
    Term in years, used when mode is 'term'.
  • fixedUntil · string · optionnel
    Optional. Rate is certain until this ISO date; beyond it the schedule is an estimate.
  • extraMonthly · number · requis
    Extra principal paid each month.

  Exemple d'appel

  {"name": "loan-payoff", "arguments": {"mode": "term", "rate": 1, "amount": 1, "startDate": "texte", "extraMonthly": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"baseline": {}, "accelerated": {}, "monthsSaved": 1, "interestSaved": 1}}

• ltv≈ 152 tokens

  Loan-to-value ratio, percent (loan / property value).

  Paramètres, retour & exemple (2)

  Paramètres

  • loanAmount · number · requis
    Loan amount.
  • propertyValue · number · requis
    Property value.

  Exemple d'appel

  {"name": "ltv", "arguments": {"loanAmount": 1, "propertyValue": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"ltvPct": 1}}

• margin-markup≈ 266 tokens

  Convert between margin and markup. Supply any one of cost/price plus one of marginPct/markupPct (or both cost and price); returns cost, price, profit, marginPct, and markupPct.

  Paramètres, retour & exemple (4)

  Paramètres

  • cost · number · optionnel
    Unit cost.
  • price · number · optionnel
    Selling price.
  • marginPct · number · optionnel
    Profit as a percent of price.
  • markupPct · number · optionnel
    Profit as a percent of cost.

  Exemple d'appel

  {"name": "margin-markup", "arguments": {"cost": 1, "price": 1, "marginPct": 1, "markupPct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"cost": 1, "price": 1, "profit": 1, "marginPct": 1, "markupPct": 1}}

• max-drawdown≈ 156 tokens

  Maximum drawdown of a value series: the largest peak-to-trough decline, as a positive percent.

  Paramètres, retour & exemple (1)

  Paramètres

  • series · array · requis
    Sequence of values (e.g. portfolio levels).

  Exemple d'appel

  {"name": "max-drawdown", "arguments": {"series": []}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"maxDrawdownPct": 1}}

• mirr≈ 215 tokens

  Modified internal rate of return: negatives financed at financeRate, positives reinvested at reinvestRate. Percents in and out.

  Paramètres, retour & exemple (3)

  Paramètres

  • cashflows · array · requis
    Cashflows by period (index 0 today; outflows negative).
  • financeRatePct · number · requis
    Finance rate in percent.
  • reinvestRatePct · number · requis
    Reinvestment rate in percent.

  Exemple d'appel

  {"name": "mirr", "arguments": {"cashflows": [], "financeRatePct": 1, "reinvestRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"mirrPct": 1}}

• mortgage-affordability≈ 334 tokens

  Maximum loan and home price the income supports: the DTI cap on gross monthly income (less existing debts) sets the payment, whose present value at the rate and term is the loan.

  Paramètres, retour & exemple (6)

  Paramètres

  • rate · number · requis
    Annual interest rate in percent.
  • dtiPct · number · requis
    Max share of gross monthly income for the payment, in percent (e.g. 36).
  • termYears · number · requis
    Loan term in years.
  • downPayment · number · optionnel
    Optional. Cash down payment, added to the loan for the home price (default 0).
  • annualIncome · number · requis
    Gross annual income.
  • monthlyDebts · number · optionnel
    Optional. Existing monthly debt payments (default 0).

  Exemple d'appel

  {"name": "mortgage-affordability", "arguments": {"rate": 1, "dtiPct": 1, "termYears": 1, "annualIncome": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"maxLoan": 1, "maxHomePrice": 1, "maxMonthlyPayment": 1}}

• net-worth≈ 142 tokens

  Net worth: assets minus liabilities.

  Paramètres, retour & exemple (2)

  Paramètres

  • assets · number · requis
    Total assets.
  • liabilities · number · requis
    Total liabilities.

  Exemple d'appel

  {"name": "net-worth", "arguments": {"assets": 1, "liabilities": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"netWorth": 1}}

• noi≈ 188 tokens

  Net operating income: gross rental income less vacancy and operating expenses.

  Paramètres, retour & exemple (3)

  Paramètres

  • vacancyPct · number · requis
    Vacancy rate in percent.
  • grossRentalIncome · number · requis
    Gross annual rental income.
  • operatingExpenses · number · requis
    Annual operating expenses.

  Exemple d'appel

  {"name": "noi", "arguments": {"vacancyPct": 1, "grossRentalIncome": 1, "operatingExpenses": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"noi": 1}}

• npv≈ 182 tokens

  Net present value of a cashflow series (index 0 is today; outflows negative) discounted at a per-period rate.

  Paramètres, retour & exemple (2)

  Paramètres

  • cashflows · array · requis
    Cashflows by period, starting at period 0. Outflows are negative.
  • discountRatePct · number · requis
    Discount rate per period in percent.

  Exemple d'appel

  {"name": "npv", "arguments": {"cashflows": [], "discountRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"npv": 1}}

• option-breakeven≈ 185 tokens

  Break-even underlying price at expiry: strike + premium for a call, strike - premium for a put.

  Paramètres, retour & exemple (3)

  Paramètres

  • type · string · optionnel · call | put
    Option type (default call).
  • strike · number · requis
    Strike price.
  • premium · number · requis
    Option premium paid.

  Exemple d'appel

  {"name": "option-breakeven", "arguments": {"strike": 1, "premium": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"breakeven": 1}}

• option-greeks≈ 338 tokens

  Black-Scholes greeks for a European option: delta, gamma, vega (per 1% vol), theta (per day), rho (per 1% rate).

  Paramètres, retour & exemple (7)

  Paramètres

  • spot · number · requis
    Current underlying price.
  • type · string · optionnel · call | put
    Option type (default call).
  • years · number · requis
    Time to expiry in years.
  • strike · number · requis
    Strike price.
  • riskFreePct · number · requis
    Risk-free rate in percent.
  • volatilityPct · number · requis
    Annualized volatility in percent.
  • dividendYieldPct · number · optionnel
    Continuous dividend yield in percent (default 0).

  Exemple d'appel

  {"name": "option-greeks", "arguments": {"spot": 1, "years": 1, "strike": 1, "riskFreePct": 1, "volatilityPct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"rho": 1, "vega": 1, "delta": 1, "gamma": 1, "theta": 1}}

• payback-period≈ 181 tokens

  Simple payback period: periods until cumulative cashflows recover the initial cost, interpolated within the crossing period. Null if never.

  Paramètres, retour & exemple (2)

  Paramètres

  • cashflows · array · requis
    Inflow each period.
  • initialCost · number · requis
    Upfront cost.

  Exemple d'appel

  {"name": "payback-period", "arguments": {"cashflows": [], "initialCost": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"years": 1}}

• percentage-change≈ 154 tokens

  Percentage change from one value to another. Null when the starting value is zero.

  Paramètres, retour & exemple (2)

  Paramètres

  • to · number · requis
    Ending value.
  • from · number · requis
    Starting value.

  Exemple d'appel

  {"name": "percentage-change", "arguments": {"to": 1, "from": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"changePct": 1}}

• perpetuity≈ 191 tokens

  Present value of a level or growing perpetuity: payment / (rate - growth). Null when growth is not below the rate.

  Paramètres, retour & exemple (3)

  Paramètres

  • payment · number · requis
    Periodic payment.
  • ratePct · number · requis
    Discount rate in percent.
  • growthPct · number · optionnel
    Optional. Payment growth rate in percent (default 0).

  Exemple d'appel

  {"name": "perpetuity", "arguments": {"payment": 1, "ratePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"pv": 1}}

• points-breakeven≈ 288 tokens

  Mortgage points break-even: the upfront cost to buy down the rate, the monthly payment saving, and the whole months to recoup it.

  Paramètres, retour & exemple (5)

  Paramètres

  • ratePct · number · requis
    Base annual rate in percent.
  • pointsPct · number · requis
    Points paid, percent of the loan.
  • loanAmount · number · requis
    Loan amount.
  • termMonths · number · requis
    Term in months.
  • reducedRatePct · number · requis
    Reduced annual rate after buying points.

  Exemple d'appel

  {"name": "points-breakeven", "arguments": {"ratePct": 1, "pointsPct": 1, "loanAmount": 1, "termMonths": 1, "reducedRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"cost": 1, "monthlySaving": 1, "breakevenMonths": 1}}

• portfolio-longevity≈ 283 tokens

  How many years a balance lasts while withdrawing from it: the balance grows each year, then the withdrawal (optionally stepping up) is taken. Returns the depletion year, or sustainable=true when it outlasts 200 years.

  Paramètres, retour & exemple (4)

  Paramètres

  • balance · number · requis
    Starting balance.
  • annualRatePct · number · requis
    Annual portfolio growth in percent.
  • annualWithdrawal · number · requis
    Amount withdrawn in the first year.
  • withdrawalGrowthPct · number · optionnel
    Optional. Yearly step-up of the withdrawal in percent (default 0).

  Exemple d'appel

  {"name": "portfolio-longevity", "arguments": {"balance": 1, "annualRatePct": 1, "annualWithdrawal": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"years": 1, "sustainable": true}}

• present-value≈ 190 tokens

  Present value of a single future amount discounted annually. The inverse of future-value.

  Paramètres, retour & exemple (3)

  Paramètres

  • years · number · requis
    Number of years until the amount is received.
  • futureAmount · number · requis
    Amount received in the future.
  • annualRatePct · number · requis
    Annual discount rate in percent.

  Exemple d'appel

  {"name": "present-value", "arguments": {"years": 1, "futureAmount": 1, "annualRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"pv": 1}}

• put-call-parity≈ 281 tokens

  Put-call parity: given one option price, returns both. Provide call or put, plus spot, strike, years, and the rate.

  Paramètres, retour & exemple (7)

  Paramètres

  • put · number · optionnel
    Put price (provide call or put).
  • call · number · optionnel
    Call price (provide call or put).
  • spot · number · requis
    Underlying price.
  • years · number · requis
    Time to expiry in years.
  • strike · number · requis
    Strike price.
  • riskFreePct · number · requis
    Risk-free rate in percent.
  • dividendYieldPct · number · optionnel
    Continuous dividend yield in percent (default 0).

  Exemple d'appel

  {"name": "put-call-parity", "arguments": {"spot": 1, "years": 1, "strike": 1, "riskFreePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"put": 1, "call": 1}}

• quick-ratio≈ 184 tokens

  Quick (acid-test) ratio: (current assets - inventory) over current liabilities.

  Paramètres, retour & exemple (3)

  Paramètres

  • inventory · number · requis
    Inventory.
  • currentAssets · number · requis
    Current assets.
  • currentLiabilities · number · requis
    Current liabilities.

  Exemple d'appel

  {"name": "quick-ratio", "arguments": {"inventory": 1, "currentAssets": 1, "currentLiabilities": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"quickRatio": 1}}

• real-return≈ 173 tokens

  Real (inflation-adjusted) return from a nominal rate via the Fisher relation: (1+nominal)/(1+inflation) - 1.

  Paramètres, retour & exemple (2)

  Paramètres

  • nominalRatePct · number · requis
    Nominal annual rate in percent.
  • inflationRatePct · number · requis
    Annual inflation in percent.

  Exemple d'appel

  {"name": "real-return", "arguments": {"nominalRatePct": 1, "inflationRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"realPct": 1}}

• refi-breakeven≈ 286 tokens

  Refinance break-even: monthly saving, whole months to recoup closing costs, and (if remainingMonths given) the net saving over the remaining term.

  Paramètres, retour & exemple (4)

  Paramètres

  • newPayment · number · requis
    New monthly payment after refinancing.
  • closingCosts · number · requis
    Upfront cost to refinance.
  • currentPayment · number · requis
    Current monthly payment.
  • remainingMonths · number · optionnel
    Optional. Months left on the loan, for the lifetime saving.

  Exemple d'appel

  {"name": "refi-breakeven", "arguments": {"newPayment": 1, "closingCosts": 1, "currentPayment": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"monthlySaving": 1, "lifetimeSaving": 1, "breakevenMonths": 1}}

• required-contribution≈ 232 tokens

  Inverse of contributions: the fixed monthly amount needed to reach a target future value over a number of months, given an optional starting balance.

  Paramètres, retour & exemple (4)

  Paramètres

  • months · number · requis
    Number of months.
  • targetValue · number · requis
    Future value goal.
  • presentValue · number · optionnel
    Optional. Starting balance (default 0).
  • annualRatePct · number · requis
    Annual growth rate in percent.

  Exemple d'appel

  {"name": "required-contribution", "arguments": {"months": 1, "targetValue": 1, "annualRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"monthly": 1}}

• required-return≈ 234 tokens

  Annual return needed to grow a starting value to a target over a number of years, optionally with a fixed annual contribution. With no contribution this equals CAGR. Returns a percent, or null when unreachable.

  Paramètres, retour & exemple (4)

  Paramètres

  • end · number · requis
    Target ending value.
  • begin · number · requis
    Starting value.
  • years · number · requis
    Number of years.
  • annualContribution · number · optionnel
    Optional. Amount added each year (default 0).

  Exemple d'appel

  {"name": "required-return", "arguments": {"end": 1, "begin": 1, "years": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"ratePct": 1}}

• return-stats≈ 216 tokens

  Mean, sample variance, and sample standard deviation (n-1) of a series of returns. Pass percents to get a percent stdev (volatility).

  Paramètres, retour & exemple (1)

  Paramètres

  • returns · array · requis
    The return series (e.g. yearly percents).

  Exemple d'appel

  {"name": "return-stats", "arguments": {"returns": []}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"mean": 1, "count": 1, "stdev": 1, "variance": 1}}

• roa≈ 152 tokens

  Return on assets, percent: net income over total assets.

  Paramètres, retour & exemple (2)

  Paramètres

  • netIncome · number · requis
    Net income.
  • totalAssets · number · requis
    Total assets.

  Exemple d'appel

  {"name": "roa", "arguments": {"netIncome": 1, "totalAssets": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"roaPct": 1}}

• roe≈ 153 tokens

  Return on equity, percent: net income over shareholders' equity.

  Paramètres, retour & exemple (2)

  Paramètres

  • equity · number · requis
    Shareholders' equity.
  • netIncome · number · requis
    Net income.

  Exemple d'appel

  {"name": "roe", "arguments": {"equity": 1, "netIncome": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"roePct": 1}}

• roi≈ 207 tokens

  Return on investment: total percent gain, plus the annualized rate when a holding period in years is given.

  Paramètres, retour & exemple (3)

  Paramètres

  • years · number · optionnel
    Optional. Holding period in years, for the annualized rate.
  • initial · number · requis
    Amount invested.
  • finalValue · number · requis
    Ending value.

  Exemple d'appel

  {"name": "roi", "arguments": {"initial": 1, "finalValue": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"roiPct": 1, "annualizedPct": 1}}

• rule-of-72≈ 154 tokens

  Years to double: the rule-of-72 estimate (72/rate) and the exact figure (ln2 / ln(1+rate)).

  Paramètres, retour & exemple (1)

  Paramètres

  • ratePct · number · requis
    Growth rate in percent.

  Exemple d'appel

  {"name": "rule-of-72", "arguments": {"ratePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"years72": 1, "exactYears": 1}}

• salary-to-hourly≈ 170 tokens

  Hourly rate implied by an annual salary.

  Paramètres, retour & exemple (3)

  Paramètres

  • annualSalary · number · requis
    Annual salary.
  • hoursPerWeek · number · optionnel
    Hours per week (default 40).
  • weeksPerYear · number · optionnel
    Weeks per year (default 52).

  Exemple d'appel

  {"name": "salary-to-hourly", "arguments": {"annualSalary": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"hourly": 1}}

• savings-rate≈ 144 tokens

  Fraction of income saved (savings divided by income). Returns a decimal.

  Paramètres, retour & exemple (2)

  Paramètres

  • income · number · requis
    Income.
  • savings · number · requis
    Amount saved.

  Exemple d'appel

  {"name": "savings-rate", "arguments": {"income": 1, "savings": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"value": 1}}

• sharpe-ratio≈ 214 tokens

  Sharpe ratio: excess mean return per unit of volatility, (mean - riskFree) / stdev. Null when volatility is undefined or zero.

  Paramètres, retour & exemple (2)

  Paramètres

  • returns · array · requis
    The return series (percents).
  • riskFreePct · number · optionnel
    Risk-free rate in the same unit (default 0).

  Exemple d'appel

  {"name": "sharpe-ratio", "arguments": {"returns": []}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"sharpe": 1, "meanPct": 1, "stdevPct": 1}}

• straight-line-depreciation≈ 200 tokens

  Straight-line depreciation: value falling evenly to a salvage value over a useful life.

  Paramètres, retour & exemple (4)

  Paramètres

  • value · number · requis
    Starting value.
  • salvage · number · requis
    Salvage value.
  • usefulYears · number · requis
    Useful life in years.
  • yearsElapsed · number · requis
    Years elapsed.

  Exemple d'appel

  {"name": "straight-line-depreciation", "arguments": {"value": 1, "salvage": 1, "usefulYears": 1, "yearsElapsed": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"value": 1}}

• successive-discounts≈ 198 tokens

  Stacked discounts applied in order: the final price and the effective single discount rate.

  Paramètres, retour & exemple (2)

  Paramètres

  • price · number · requis
    Original price.
  • discountsPct · array · requis
    Discounts in percent, applied in order.

  Exemple d'appel

  {"name": "successive-discounts", "arguments": {"price": 1, "discountsPct": []}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"finalPrice": 1, "effectivePct": 1}}

• sum-of-years-digits≈ 220 tokens

  Sum-of-the-years'-digits depreciation: the depreciable base weighted toward the early years.

  Paramètres, retour & exemple (4)

  Paramètres

  • year · number · requis
    Year (1-based).
  • value · number · requis
    Initial cost.
  • salvage · number · requis
    Salvage value.
  • usefulYears · number · requis
    Useful life in years.

  Exemple d'appel

  {"name": "sum-of-years-digits", "arguments": {"year": 1, "value": 1, "salvage": 1, "usefulYears": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"bookValue": 1, "depreciation": 1}}

• tax-equivalent-yield≈ 182 tokens

  Tax-equivalent yield: the taxable yield that matches a tax-free (e.g. muni) yield. Percents in and out.

  Paramètres, retour & exemple (2)

  Paramètres

  • taxRatePct · number · requis
    Marginal tax rate in percent.
  • taxFreeYieldPct · number · requis
    Tax-free yield in percent.

  Exemple d'appel

  {"name": "tax-equivalent-yield", "arguments": {"taxRatePct": 1, "taxFreeYieldPct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"taxEquivalentPct": 1}}

• tax-from-brackets≈ 291 tokens

  Progressive tax from caller-supplied brackets. No jurisdiction, year, or rates are baked in: pass the brackets yourself. Returns total tax, effective rate, and marginal rate.

  Paramètres, retour & exemple (2)

  Paramètres

  • income · number · requis
    Taxable income.
  • brackets · array · requis
    Ordered tax bands. The final band may omit upTo to run to infinity.

  Exemple d'appel

  {"name": "tax-from-brackets", "arguments": {"income": 1, "brackets": []}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"tax": 1, "marginalRatePct": 1, "effectiveRatePct": 1}}

• tip-split≈ 196 tokens

  Tip and split: the tip amount, the total, and the per-person share.

  Paramètres, retour & exemple (3)

  Paramètres

  • people · number · optionnel
    Number of people (default 1).
  • tipPct · number · requis
    Tip in percent.
  • billAmount · number · requis
    Bill amount.

  Exemple d'appel

  {"name": "tip-split", "arguments": {"tipPct": 1, "billAmount": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"tip": 1, "total": 1, "perPerson": 1}}

• unit-price≈ 156 tokens

  Unit price: price divided by quantity (for comparing pack sizes). Null when quantity is zero.

  Paramètres, retour & exemple (2)

  Paramètres

  • price · number · requis
    Price.
  • quantity · number · requis
    Quantity / size.

  Exemple d'appel

  {"name": "unit-price", "arguments": {"price": 1, "quantity": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"unitPrice": 1}}

• units-of-production-depreciation≈ 231 tokens

  Units-of-production depreciation: the depreciable base spread over total expected units, charged by the units used this period.

  Paramètres, retour & exemple (4)

  Paramètres

  • value · number · requis
    Initial cost.
  • salvage · number · requis
    Salvage value.
  • totalUnits · number · requis
    Total expected units over the life.
  • unitsThisPeriod · number · requis
    Units produced this period.

  Exemple d'appel

  {"name": "units-of-production-depreciation", "arguments": {"value": 1, "salvage": 1, "totalUnits": 1, "unitsThisPeriod": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"depreciation": 1}}

• vat≈ 244 tokens

  Value-added tax (MwSt/USt, sales tax) on a price. By default adds the tax to a net price; with inclusive=true treats the amount as gross and extracts the tax. The rate is always an input (19 or 7 for Germany, etc.).

  Paramètres, retour & exemple (3)

  Paramètres

  • amount · number · requis
    The price.
  • ratePct · number · requis
    VAT rate in percent (e.g. 19 or 7).
  • inclusive · boolean · optionnel
    false (default): amount is net, add the tax. true: amount is gross, extract the tax.

  Exemple d'appel

  {"name": "vat", "arguments": {"amount": 1, "ratePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"net": 1, "tax": 1, "gross": 1}}

• wacc≈ 231 tokens

  Weighted average cost of capital: equity and after-tax debt weighted by the capital structure. Percents in and out.

  Paramètres, retour & exemple (5)

  Paramètres

  • debt · number · requis
    Market value of debt.
  • equity · number · requis
    Market value of equity.
  • taxRatePct · number · requis
    Tax rate in percent.
  • costDebtPct · number · requis
    Cost of debt in percent.
  • costEquityPct · number · requis
    Cost of equity in percent.

  Exemple d'appel

  {"name": "wacc", "arguments": {"debt": 1, "equity": 1, "taxRatePct": 1, "costDebtPct": 1, "costEquityPct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"waccPct": 1}}

• xirr≈ 209 tokens

  Date-aware internal rate of return: the annual rate that zeroes the XNPV of irregular dated cashflows. Null if no rate fits.

  Paramètres, retour & exemple (1)

  Paramètres

  • cashflows · array · requis
    Dated cashflows; the first date is the valuation date.

  Exemple d'appel

  {"name": "xirr", "arguments": {"cashflows": []}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"xirrPct": 1}}

• xnpv≈ 236 tokens

  Date-aware net present value: each amount discounted by its fractional years (act/365) from the first cashflow's date. Annual rate in percent.

  Paramètres, retour & exemple (2)

  Paramètres

  • cashflows · array · requis
    Dated cashflows; the first date is the valuation date.
  • annualRatePct · number · requis
    Annual discount rate in percent.

  Exemple d'appel

  {"name": "xnpv", "arguments": {"cashflows": [], "annualRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"npv": 1}}

• yield-to-maturity≈ 266 tokens

  Bond yield to maturity: the nominal annual yield that prices a bond at the given price, with periodic coupons and face returned at maturity. Solved numerically. Returns a percent, or null.

  Paramètres, retour & exemple (5)

  Paramètres

  • price · number · requis
    Current bond price.
  • years · number · requis
    Years to maturity.
  • faceValue · number · requis
    Face (par) value repaid at maturity.
  • couponRatePct · number · requis
    Annual coupon rate in percent of face.
  • periodsPerYear · number · optionnel
    Coupon periods per year (default 2 = semiannual).

  Exemple d'appel

  {"name": "yield-to-maturity", "arguments": {"price": 1, "years": 1, "faceValue": 1, "couponRatePct": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"yieldPct": 1}}

• zero-coupon-price≈ 198 tokens

  Price of a zero-coupon bond: face value discounted to today at the yield.

  Paramètres, retour & exemple (4)

  Paramètres

  • years · number · requis
    Years to maturity.
  • yieldPct · number · requis
    Annual yield in percent.
  • faceValue · number · requis
    Face value.
  • compoundingPerYear · number · optionnel
    Compounding periods per year (default 1).

  Exemple d'appel

  {"name": "zero-coupon-price", "arguments": {"years": 1, "yieldPct": 1, "faceValue": 1}}

  Exemple de retour

  {"content": [{"type": "text", "text": "…"}], "structuredContent": {"price": 1}}

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