Notepad

Regular payment that pays off a loan or saves up to a target amount (Excel: PMT). Money paid out is negative, money received positive.

• rate – interest rate per period, e.g. 3.6% / 12 for monthly payments
• periods – number of payments, e.g. 30 * 12
• pv – amount today, e.g. -loan
• fv (optional, default 0) – balance left after the last payment
• type (optional, default 0) – 0 = payment at the end of the period, 1 = at the beginning

Example: PMT(3.6% / 12, 30 * 12, -400,000) · also pmt

Value of an investment or loan after all periods (Excel: FV), e.g. the final balance of a savings plan.

• rate – interest rate per period
• periods – number of periods
• payment – payment per period, paid in = negative
• pv (optional, default 0) – starting amount, paid in = negative
• type (optional, default 0) – 0 = payment at the end of the period, 1 = at the beginning

Example: FV(5% / 12, 20 * 12, -200, -10,000) · also fv

What future payments are worth today (Excel: PV), e.g. how large a loan a monthly payment can afford.

• rate – interest rate per period
• periods – number of periods
• payment – payment per period
• fv (optional, default 0) – amount after the last period
• type (optional, default 0) – 0 = payment at the end of the period, 1 = at the beginning

Example: PV(3.6% / 12, 30 * 12, -1,500) · also pv

How many payments are needed, e.g. until a loan is paid off (Excel: NPER).

• rate – interest rate per period
• payment – payment per period, paid = negative
• pv – amount today, e.g. the loan
• fv (optional, default 0) – target amount after the last period
• type (optional, default 0) – 0 = payment at the end of the period, 1 = at the beginning

Example: NPER(3.6% / 12, -2,000, 400,000) / 12 · also nper

The interest rate that matches term, payment and amount (Excel: RATE). Times 12 gives the annual rate for monthly payments.

• periods – number of periods
• payment – payment per period, paid = negative
• pv – amount today
• fv (optional, default 0) – amount after the last period
• type (optional, default 0) – 0 = payment at the end of the period, 1 = at the beginning

Example: RATE(30 * 12, -1,800, 400,000) * 12 · also rate

Payment of an annuity loan from the nominal interest rate and the initial repayment rate, as banks typically quote it.

• loan – loan amount
• rate – nominal interest rate per year
• repayment – initial repayment rate per year
• payments per year (optional, default 12) – 12 = monthly, 4 = quarterly, 1 = yearly

Example: ANNUITY(400,000, 3.6%, 2%) · also annuityPayment

Converts a nominal rate compounded several times a year into the effective annual rate (APY).

• nominal rate – nominal annual rate
• periods per year (optional, default 12) – compounding periods per year

Example: EFFECT(3.6%) · also effectiveRate

Present value of regular payments at the end of each period (Excel: NPV – the first payment is already discounted).

• rate – discount rate per period
• payments – payments of periods 1, 2, …

Example: NPV(10%, -€10,000, €3,000, €4,200, €6,800) · also npv, NBW

Return of regular payments (Excel: IRR). The first payment is usually the (negative) investment.

• payments – payments at equal intervals, at least one negative and one positive

Example: IRR(-70,000, 12,000, 15,000, 18,000, 21,000, 26,000) · also irr, IKV

Annual return of payments on any days (Excel: XIRR). Give amount and date alternately.

• amount, date – pairs of payment and date, e.g. -10,000, 2026-01-01

Example: XIRR(-10,000, 2025-01-01, 4,000, 2026-01-01, 7,000, 2026-07-01) · also xirr, XINTZINSFUSS

Present value of payments on any days, discounted to the first date (Excel: XNPV).

• rate – annual discount rate
• amount, date – pairs of payment and date

Example: XNPV(5%, -10,000, 2025-01-01, 4,000, 2026-01-01, 7,000, 2026-07-01) · also xnpv, XKAPITALWERT

Converts an effective annual rate back into the nominal rate compounded several times a year.

• effective rate – effective annual rate
• periods per year (optional, default 12) – compounding periods per year

Example: NOMINAL(3.66%) · also nominalRate

German income tax on taxable income, 2024–2026 rates. In words: “income tax on €50,000 married”.

• income – taxable income per year
• joint (optional, default 0) – 1 = joint assessment (income splitting)
• year (optional, default 2026) – tax year, e.g. 2025

Example: incomeTax(€50,000) · also EINKOMMENSTEUER

5.5% of the income tax above the exemption limit (2026: €20,350, joint €40,700), with a phase-in zone.

• incomeTax – assessed income tax
• joint (optional, default 0) – 1 = joint assessment
• year (optional, default 2026) – tax year

Example: solidaritySurcharge(€30,000) · also SOLI

9% of the income tax, 8% in Bavaria and Baden-Wuerttemberg.

• incomeTax – assessed income tax
• rate (optional, default 9 %) – 9% or 8%

Example: churchTax(€10,000, 8%) · also KIRCHENSTEUER

taxRate: income tax divided by taxable income. marginalTaxRate: tax on each additional euro. In words: “tax rate for €60,000”, “marginal tax rate for €60,000”.

• income – taxable income
• joint (optional, default 0) – 1 = joint assessment
• year (optional, default 2026) – tax year

Example: taxRate(€60,000) · also marginalTaxRate, STEUERSATZ, GRENZSTEUERSATZ

25% flat tax on investment income above the saver’s allowance, including solidarity surcharge and optionally church tax.

• gains – investment income per year
• allowance (optional, default 1.000 €) – saver’s allowance: €1,000, married €2,000
• churchTaxRate (optional, default 0) – 0, 8% or 9%

Example: capitalGainsTax(€5,000) · also ABGELTUNGSTEUER

Adds up all values. Without parentheses, “sum” totals the current block.

• values – any number of numbers or variables, separated by commas

Example: SUM(120, 80, 45.50) · also sum

Arithmetic mean of all values.

• values – any number of numbers or variables

Example: AVERAGE(1,200, 1,350, 1,180) · also avg

The middle value of the sorted values – robust against outliers.

• values – any number of numbers or variables

Example: MEDIAN(1,200, 1,350, 4,000) · also median

Sample standard deviation (like STDEV.S in Excel), at least two values.

• values – any number of numbers or variables

Example: STDEV(20, 30, 40) · also stdev

Number of values, or the rows of a table.

• values – numbers, variables or a table

Example: COUNT(3, 5, 8) · also count

The smallest of the given values.

• values – any number of numbers or variables

Example: MIN(3.6%, 3.9%, 3.4%) · also min

The largest of the given values.

• values – any number of numbers or variables

Example: MAX(0, 2,500 - 3,100) · also max

Rounds half away from zero to the given number of decimal places.

• number – the value to round
• digits (optional, default 0) – decimal places; negative rounds to tens, hundreds …

Example: ROUND(1,234.567, 2) · also round

The value without its sign, handy for negative payments.

• number – any value

Example: ABS(-1,817.94) · also abs

The square root of a non-negative number.

• number – non-negative value

Example: SQRT(144) · also sqrt

Base raised to the exponent, the same as base ^ exponent.

• base – the number raised to a power
• exponent – the power

Example: pow(1.05, 10)

Rounds down to the next smaller whole number.

• number – any value

Example: floor(7.8)

Rounds up to the next larger whole number.

• number – any value

Example: ceil(7.2)

Keeps a value between a lower and an upper limit.

• number – the value to limit
• min – lower limit
• max – upper limit

Example: clamp(12%, 0%, 10%)

e to the power of x, e.g. for continuous compounding.

• x – exponent

Example: exp(0.05)

Logarithm to base e.

• x – positive value

Example: ln(2) / ln(1.05)

Logarithm to base 10.

• x – positive value

Example: log10(1,000)

Logarithm to any base (without a base: 10). In words: “log 64 base 4” or “81 is 9 to what power”.

• number – positive value
• base (optional, default 10) – base of the logarithm

Example: LOG(64, 4) · also log

Logarithm to base 2.

• x – positive value

Example: log2(1,024)

The n-th root of a number. In words: “3rd root of 27”, “cube root of 27”, “square root of 81” or “√81”.

• number – the radicand
• n – degree of the root, e.g. 3 for the cube root

Example: root(1.5, 10)

The third root of a number.

• number – any value

Example: CBRT(27) · also cbrt

n! = 1 · 2 · … · n, also written “5!” or “factorial of 5”.

• n – whole number ≥ 0

Example: FACT(5) · also fact

The greatest common divisor of whole numbers, also “gcd of 12 and 18”.

• numbers – whole numbers

Example: GCD(12, 18) · also gcd

The least common multiple of whole numbers, also “lcm of 4 and 6”.

• numbers – whole numbers

Example: LCM(4, 6) · also lcm

Sine, cosine, tangent and their inverses in radians (pi = 180°).

• x – angle in radians

Example: sin(pi / 6) · also cos, tan, asin, acos, atan