amortization
Amortization Schedule
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.
输入参数mode必填rate必填extralimitamount必填detailoffsetpaymentrateStepsstartDate必填termYearsfixedUntil
Time and interest saved by paying a fixed extra amount every month on a loan, versus the baseline schedule.
输入参数mode必填rate必填extraamount必填paymentstartDate必填termYearsfixedUntilextraMonthly必填
Future value of a single lump sum compounded annually.
输入参数years必填principal必填annualRatePct必填
contributions
Future Value of Contributions
Future value of a fixed monthly contribution, optionally stepping up each year.
输入参数months必填monthly必填annualRatePct必填contribGrowthPct
Compound annual growth rate between two values over a number of years. Returns a decimal (0.07 means 7%).
输入参数end必填begin必填years必填
Fraction of income saved (savings divided by income). Returns a decimal.
输入参数income必填savings必填
Convert an amount using a rate supplied by the caller (units of target currency per unit of source). No rate is ever looked up.
输入参数rate必填amount必填
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.
输入参数upvalue必填years必填annualRatePct必填
straight-line-depreciation
Straight-Line Depreciation
Straight-line depreciation: value falling evenly to a salvage value over a useful life.
输入参数value必填salvage必填usefulYears必填yearsElapsed必填
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.
输入参数annualSpend必填annualRatePctcurrentNestEggwithdrawalRatePctannualContribution
required-contribution
Required Contribution
Inverse of contributions: the fixed monthly amount needed to reach a target future value over a number of months, given an optional starting balance.
输入参数months必填targetValue必填presentValueannualRatePct必填
inflation-adjust
Inflation Adjust
Convert a nominal amount to today's purchasing power (real), or with toNominal inflate a real amount forward, at a given annual inflation rate.
输入参数years必填amount必填toNominalinflationRatePct必填
effective-rate
Effective Rate
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.
输入参数ratePct必填toNominalperiodsPerYear必填
Net present value of a cashflow series (index 0 is today; outflows negative) discounted at a per-period rate.
输入参数cashflows必填discountRatePct必填
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.
输入参数cashflows必填
refi-breakeven
Refinance Break-Even
Refinance break-even: monthly saving, whole months to recoup closing costs, and (if remainingMonths given) the net saving over the remaining term.
输入参数newPayment必填closingCosts必填currentPayment必填remainingMonths
emergency-fund
Emergency Fund
Months of runway: liquid savings divided by monthly expenses.
输入参数liquidSavings必填monthlyExpenses必填
mortgage-affordability
Mortgage Affordability
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.
输入参数rate必填dtiPct必填termYears必填downPaymentannualIncome必填monthlyDebts
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.
输入参数debts必填methodmonthlyBudget必填
portfolio-longevity
Portfolio Longevity
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.
输入参数balance必填annualRatePct必填annualWithdrawal必填withdrawalGrowthPct
present-value
Present Value
Present value of a single future amount discounted annually. The inverse of future-value.
输入参数years必填futureAmount必填annualRatePct必填
required-return
Required Return
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.
输入参数end必填begin必填years必填annualContribution
yield-to-maturity
Yield to Maturity
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.
输入参数price必填years必填faceValue必填couponRatePct必填periodsPerYear
tax-from-brackets
Tax from Brackets
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.
输入参数income必填brackets必填
margin-markup
Margin & Markup
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.
输入参数costpricemarginPctmarkupPct
compound-interest
Compound Interest
Compound growth at any frequency, with an optional contribution each period (paid at period end). Generalizes future-value (periodsPerYear 1) and contributions (periodsPerYear 12).
输入参数years必填principal必填annualRatePct必填periodsPerYearcontributionPerPeriod
de-gross-to-net
German Gross-to-Net (manual figures)
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).
输入参数soligross必填carePcthealthPctincomeTaxpensionPctchurchTaxPcthealthCeilingpensionCeilingunemploymentPct
de-net-salary
German Net Salary (exact, by tax year)
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.
输入参数ageyear必填faktorchildrentaxClassbundeslandgrossAnnual必填kvZusatzPctchurchTaxPctprivateHealthchildrenUnder25
de-abgeltungsteuer
German Capital Gains Tax (Abgeltungsteuer)
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.
输入参数year必填jointchurchTaxPctcapitalIncome必填foreignTaxCredit
de-kindergeld
German Child Benefit (Kindergeld)
German child benefit (Kindergeld) for 2023-2026: the year's flat monthly amount per child (uniform since 2023), as monthly and annual totals.
输入参数year必填children
de-midijob
German Midijob Contributions
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.
输入参数ageyear必填childrenbundeslandmonthlyPay必填kvZusatzPctchildrenUnder25
de-rentenpunkte
German Pension Points (Rentenpunkte)
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.
输入参数year必填bundeslandgrossAnnual必填totalPoints
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.).
输入参数amount必填ratePct必填inclusive
Return on investment: total percent gain, plus the annualized rate when a holding period in years is given.
输入参数yearsinitial必填finalValue必填
Real (inflation-adjusted) return from a nominal rate via the Fisher relation: (1+nominal)/(1+inflation) - 1.
输入参数nominalRatePct必填inflationRatePct必填
return-stats
Return Statistics
Mean, sample variance, and sample standard deviation (n-1) of a series of returns. Pass percents to get a percent stdev (volatility).
输入参数returns必填
Sharpe ratio: excess mean return per unit of volatility, (mean - riskFree) / stdev. Null when volatility is undefined or zero.
输入参数returns必填riskFreePct
Maximum drawdown of a value series: the largest peak-to-trough decline, as a positive percent.
输入参数series必填
holding-period-return
Holding Period Return
Holding-period return: (income + capital gain) / starting value, in percent.
输入参数income必填endValue必填beginValue必填
Effect of an annual fee: the compounded balance at the gross rate vs net of the fee, and the amount lost to fees.
输入参数years必填feePct必填principal必填grossAnnualPct必填
dollar-cost-averaging
Dollar-Cost Averaging
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.
输入参数prices必填periodicInvestment必填
Price of a coupon bond given a yield: present value of the coupons plus the face at maturity.
输入参数years必填yieldPct必填faceValue必填couponRatePct必填periodsPerYear
current-yield
Current Yield
Current yield: the annual coupon as a percent of the bond's current price.
输入参数price必填faceValue必填couponRatePct必填
bond-duration
Bond Duration
Macaulay duration (PV-weighted average time of cashflows, in years) and modified duration (price sensitivity to yield).
输入参数years必填yieldPct必填faceValue必填couponRatePct必填periodsPerYear
Bond convexity (years^2): the curvature of price with respect to yield, used alongside duration.
输入参数years必填yieldPct必填faceValue必填couponRatePct必填periodsPerYear
zero-coupon-price
Zero-Coupon Price
Price of a zero-coupon bond: face value discounted to today at the yield.
输入参数years必填yieldPct必填faceValue必填compoundingPerYear
accrued-interest
Accrued Interest
Accrued interest since the last coupon: the annual coupon pro-rated by days elapsed over the day-count basis.
输入参数faceValue必填couponRatePct必填dayCountBasisdaysSinceLastCoupon必填
black-scholes
Black-Scholes Option Price
Black-Scholes price of a European call or put option, plus d1/d2. Volatility and rates in percent; optional continuous dividend yield.
输入参数spot必填typeyears必填strike必填riskFreePct必填volatilityPct必填dividendYieldPct
option-greeks
Option Greeks
Black-Scholes greeks for a European option: delta, gamma, vega (per 1% vol), theta (per day), rho (per 1% rate).
输入参数spot必填typeyears必填strike必填riskFreePct必填volatilityPct必填dividendYieldPct
put-call-parity
Put-Call Parity
Put-call parity: given one option price, returns both. Provide call or put, plus spot, strike, years, and the rate.
输入参数putcallspot必填years必填strike必填riskFreePct必填dividendYieldPct
option-breakeven
Option Break-Even
Break-even underlying price at expiry: strike + premium for a call, strike - premium for a put.
输入参数typestrike必填premium必填
intrinsic-time-value
Intrinsic & Time Value
Split an option premium into intrinsic value (in-the-money amount) and time value.
输入参数spot必填typestrike必填premium必填
annuity-pv
Annuity Present Value
Present value of an ordinary annuity (level payment at each period end). rate is the per-period rate in percent.
输入参数payment必填periods必填ratePct必填
annuity-fv
Annuity Future Value
Future value of an ordinary annuity. rate is the per-period rate in percent.
输入参数payment必填periods必填ratePct必填
annuity-payment
Annuity Payment
The level payment that amortizes a present value over n periods (the loan-payment formula). rate is per period.
输入参数periods必填ratePct必填presentValue必填
Present value of a level or growing perpetuity: payment / (rate - growth). Null when growth is not below the rate.
输入参数payment必填ratePct必填growthPct
Years to double: the rule-of-72 estimate (72/rate) and the exact figure (ln2 / ln(1+rate)).
输入参数ratePct必填
payback-period
Payback Period
Simple payback period: periods until cumulative cashflows recover the initial cost, interpolated within the crossing period. Null if never.
输入参数cashflows必填initialCost必填
discounted-payback
Discounted Payback
Discounted payback period: like payback-period but each cashflow is discounted at the per-period rate.
输入参数ratePct必填cashflows必填initialCost必填
Modified internal rate of return: negatives financed at financeRate, positives reinvested at reinvestRate. Percents in and out.
输入参数cashflows必填financeRatePct必填reinvestRatePct必填
Date-aware net present value: each amount discounted by its fractional years (act/365) from the first cashflow's date. Annual rate in percent.
输入参数cashflows必填annualRatePct必填
Date-aware internal rate of return: the annual rate that zeroes the XNPV of irregular dated cashflows. Null if no rate fits.
输入参数cashflows必填
Effective APR including upfront fees: the note-rate payment priced against the net proceeds (amount - fees). Annual percent.
输入参数feesamount必填ratePct必填termMonths必填
interest-only-payment
Interest-Only Payment
Interest-only monthly payment on a balance.
输入参数amount必填ratePct必填
Balloon loan: payment based on a long amortization, with the balloon being the balance still due after the shorter balloon term.
输入参数amount必填ratePct必填amortMonths必填balloonMonths必填
Loan-to-value ratio, percent (loan / property value).
输入参数loanAmount必填propertyValue必填
Debt-to-income ratio, percent (monthly debt / gross monthly income).
输入参数monthlyDebt必填grossMonthlyIncome必填
credit-card-payoff
Credit Card Payoff
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.
输入参数aprPct必填balance必填monthlyPayment必填
points-breakeven
Points Break-Even
Mortgage points break-even: the upfront cost to buy down the rate, the monthly payment saving, and the whole months to recoup it.
输入参数ratePct必填pointsPct必填loanAmount必填termMonths必填reducedRatePct必填
biweekly-payoff
Biweekly Payoff
Biweekly mortgage acceleration: paying half the monthly payment every two weeks. Returns the biweekly payment and the months and interest saved.
输入参数amount必填ratePct必填termMonths必填
Capitalization rate: net operating income as a percent of property value.
输入参数noi必填propertyValue必填
cash-on-cash
Cash-on-Cash Return
Cash-on-cash return: annual pre-tax cash flow as a percent of the cash invested.
输入参数cashInvested必填annualCashFlow必填
Net operating income: gross rental income less vacancy and operating expenses.
输入参数vacancyPct必填grossRentalIncome必填operatingExpenses必填
gross-rent-multiplier
Gross Rent Multiplier
Gross rent multiplier: price divided by gross annual rent.
输入参数price必填grossAnnualRent必填
dscr
Debt Service Coverage Ratio
Debt service coverage ratio: net operating income divided by annual debt service.
输入参数noi必填annualDebtService必填
Weighted average cost of capital: equity and after-tax debt weighted by the capital structure. Percents in and out.
输入参数debt必填equity必填taxRatePct必填costDebtPct必填costEquityPct必填
break-even-units
Break-Even Units
Break-even volume: fixed costs divided by the per-unit contribution (price - variable cost), plus the revenue at that volume.
输入参数fixedCosts必填pricePerUnit必填variableCostPerUnit必填
contribution-margin
Contribution Margin
Contribution margin per unit and as a percent of price.
输入参数pricePerUnit必填variableCostPerUnit必填
current-ratio
Current Ratio
Current ratio: current assets over current liabilities.
输入参数currentAssets必填currentLiabilities必填
Quick (acid-test) ratio: (current assets - inventory) over current liabilities.
输入参数inventory必填currentAssets必填currentLiabilities必填
Return on equity, percent: net income over shareholders' equity.
输入参数equity必填netIncome必填
Return on assets, percent: net income over total assets.
输入参数netIncome必填totalAssets必填
declining-balance-depreciation
Declining-Balance Depreciation
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.
输入参数year必填value必填ratePct必填
double-declining-depreciation
Double-Declining Depreciation
Double-declining-balance depreciation: 2/usefulYears of the book value each year, not falling below salvage.
输入参数year必填value必填salvageusefulYears必填
sum-of-years-digits
Sum-of-Years' Digits Depreciation
Sum-of-the-years'-digits depreciation: the depreciable base weighted toward the early years.
输入参数year必填value必填salvage必填usefulYears必填
units-of-production-depreciation
Units-of-Production Depreciation
Units-of-production depreciation: the depreciable base spread over total expected units, charged by the units used this period.
输入参数value必填salvage必填totalUnits必填unitsThisPeriod必填
Net worth: assets minus liabilities.
输入参数assets必填liabilities必填
budget-50-30-20
50/30/20 Budget Split
The 50/30/20 budget split of monthly income into needs, wants, and savings.
输入参数monthlyIncome必填
Tip and split: the tip amount, the total, and the per-person share.
输入参数peopletipPct必填billAmount必填
A single percentage discount: the amount off and the final price.
输入参数price必填discountPct必填
successive-discounts
Successive Discounts
Stacked discounts applied in order: the final price and the effective single discount rate.
输入参数price必填discountsPct必填
percentage-change
Percentage Change
Percentage change from one value to another. Null when the starting value is zero.
输入参数to必填from必填
Unit price: price divided by quantity (for comparing pack sizes). Null when quantity is zero.
输入参数price必填quantity必填
hourly-to-salary
Hourly to Salary
Annualize an hourly rate (and the monthly equivalent).
输入参数hourlyRate必填hoursPerWeekweeksPerYear
salary-to-hourly
Salary to Hourly
Hourly rate implied by an annual salary.
输入参数annualSalary必填hoursPerWeekweeksPerYear
after-tax-yield
After-Tax Yield
After-tax yield: a yield reduced by the tax rate. Percents in and out.
输入参数yieldPct必填taxRatePct必填
tax-equivalent-yield
Tax-Equivalent Yield
Tax-equivalent yield: the taxable yield that matches a tax-free (e.g. muni) yield. Percents in and out.
输入参数taxRatePct必填taxFreeYieldPct必填
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.
输入参数annualSpend必填annualRatePct必填currentNestEgg必填withdrawalRatePctyearsToRetirement必填
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.
输入参数annualSpend必填partTimeIncome必填withdrawalRatePct