Percentage & finance cheat sheet

Percent / Percentage

A number expressed as a fraction of 100. 25% means 25 out of 100, or 0.25 in decimal form.

Percentage point

The absolute difference between two percentages, not a percent change. A move from 5% to 7% is a 2 percentage-point increase — but a 40% relative increase.

Basis point (bp)

One one-hundredth of a percentage point. 50 basis points = 0.50%. Used to talk about interest rate changes precisely.

Percent change

The relative change between two values. Positive for increase, negative for decrease.

Reverse percentage

Finding the original number when you know the result and the percentage applied.

Stacked / compound discount

Two or more discounts applied in sequence. They do not simply add — they multiply on the remaining percentages.

Per mille (‰)

Per thousand, analogous to percent but on base 1000. 25‰ = 2.5%. Used in alcohol concentration and some tax rates.

Mean

The arithmetic average — sum of all values divided by the count.

Median

The middle value when data is sorted. Robust to outliers in a way the mean isn't.

Mode

The most frequently occurring value in a dataset.

Percentile

The value below which a given percentage of observations fall. The 90th percentile is the value below which 90% of data sits.

Quartile

Values that divide a sorted dataset into four equal parts: Q1 (25th percentile), Q2 (median), Q3 (75th percentile).

IQR (Interquartile range)

The middle 50% of the data: Q3 minus Q1. Used to spot outliers and measure spread.

Standard deviation

A measure of how spread out values are from the mean. Larger SD = more variability.

Weighted average

An average where each value has a different weight. Used in portfolio returns and grade calculations.

Simple interest

Interest calculated only on the original principal, not on accumulated interest.

Compound interest

Interest calculated on the principal plus previously accumulated interest. Grows faster than simple interest over time.

APR (Annual Percentage Rate)

The yearly cost of a loan or credit, expressed as a percentage. Includes interest but not all fees.

APY / AER

Annual percentage yield (US) / annual equivalent rate (UK). The true annual return after compounding is factored in.

ROI (Return on Investment)

The percentage gain or loss on an investment, relative to its cost.

IRR (Internal Rate of Return)

The discount rate at which the net present value of cash flows is zero. Used to compare investments with different timing.

CAGR

Compound Annual Growth Rate — the smoothed annualized growth rate over a multi-year period.

NPV (Net Present Value)

The current value of future cash flows, discounted at a chosen rate. Positive NPV means the investment is worth pursuing.

EMI

Equated Monthly Installment — fixed monthly payment on a loan that combines principal and interest.

Amortization

The process of paying off a loan in regular installments where each payment covers a shrinking portion of interest and growing portion of principal.

Principal

The original amount of money borrowed or invested, before any interest accrues.

Yield

The income return on an investment, typically expressed as a percentage of cost or current price.

Inflation

The percentage rate at which a basket of goods rises in price over time. Erodes the purchasing power of money.

Real vs nominal

Nominal is the headline number; real is the number adjusted for inflation. Real return is what your money actually bought you.

Profit margin

Profit as a percentage of revenue. Higher is better.

Markup

The amount added to cost to set the selling price, expressed as a percentage of cost (not revenue). Often confused with margin.

Gross margin

Revenue minus the direct cost of goods sold, expressed as a percentage of revenue.

Net margin

The bottom-line margin after all expenses, taxes and interest are subtracted.

Conversion rate

The percentage of visitors who complete a desired action (purchase, signup, click).

Churn rate

The percentage of customers who cancel or stop using a service over a given period.

Customer lifetime value (LTV)

The total revenue a typical customer generates over their relationship with the business.

CAC (Customer Acquisition Cost)

The total cost of marketing and sales divided by the number of new customers acquired in the same period.

Market share

A company's sales as a percentage of total industry sales.

VAT (Value Added Tax)

A consumption tax applied to goods and services at each stage of the supply chain. Used across the EU, UK and most of the world outside the US.

Sales tax

A consumption tax applied at the point of final sale only. Used in the US (varies by state) and a few other countries.

GST (Goods and Services Tax)

A national consumption tax used in countries like India, Canada, Australia, Singapore and New Zealand. Mechanism similar to VAT.

Net price

The price before tax is added. What the seller actually receives.

Gross price

The price including tax. What the buyer pays at the till.

Tip percentage

A gratuity expressed as a percentage of the pre-tax bill. Typical US tip is 18–20% on the pre-tax total.

Discount percentage

A reduction in the original price expressed as a percent. The "you save" line.

Dynamic currency conversion (DCC)

The "pay in your home currency or local" prompt at a foreign card terminal. Always pick local currency — DCC adds a 4–8% markup.

10% shortcut

Move the decimal point one place to the left. 10% of 347 = 34.7.

5% shortcut

Half of 10%. 5% of 347 = 17.35.

15% shortcut

10% + 5%. 15% of 347 = 34.7 + 17.35 = 52.05.

20% shortcut

Double 10%. 20% of 347 = 69.4.

25% shortcut

Divide by 4. 25% of 347 = 86.75.

50% shortcut

Divide by 2.

75% shortcut

Three-quarters: original × 3 ÷ 4.

X% of Y = Y% of X

A surprising identity. 4% of 75 is the same as 75% of 4 — both equal 3. Sometimes the reversed form is easier to compute.

Rule of 72

Estimate how many years it takes money to double at a given annual return: divide 72 by the percentage rate. At 7%, money doubles in about 10.3 years.

Rule of 70

Variant of Rule of 72 — sometimes a closer approximation at lower rates. Same idea: divide 70 by the rate to get doubling time.