Business Math: Make Confident Decisions with Numbers

Master the most commonly used number format in business. This lecture covers the three fundamental percentage calculations, percentage change, successive percentage traps, common equivalents, and real-world applications from profit margins to revenue waterfalls.

What You Will Learn:

- What a percentage means visually (100-square grid)

- Three fundamental calculations: find %, find the part, find the whole

- Sell-through rate calculation with inventory bar visualization

- Percentage change formula for tracking business performance

- Why successive +20% then -20% does NOT return to the original (different base trap)

- Common percentage-fraction-decimal equivalents reference table

- Revenue to net profit waterfall calculation (COGS, OpEx, Tax)

- Profit margin comparison across companies of different sizes

Go deeper into percentage calculations that drive every business performance metric. This lecture covers increase/decrease multipliers, the percentage change formula, reversing changes, multi-period compounding, CAGR, and the critical distinction between percentage points and percentages.

What You Will Learn:

- Percentage increase using the (1 + rate) multiplier with bar visualization

- Percentage decrease using the (1 − rate) multiplier

- The percentage change formula with three worked examples

- How to reverse a percentage change to find the original value

- Multi-period percentage changes that compound (not add)

- CAGR (Compound Annual Growth Rate) formula and graph

- Percentage points vs percentages — additive vs multiplicative measures

- Complete worked problem: month-over-month sales analysis

Master the three pricing concepts that every business professional must know. This lecture clearly distinguishes markup from margin, shows conversion formulas, demonstrates successive discount traps, and introduces the break-even discount concept.

What You Will Learn:

- Markup: profit as a percentage of cost

- Margin: profit as a percentage of selling price

- Why markup is always larger than margin for the same product

- Conversion formulas: markup ↔ margin

- Discount calculations on a number line

- Successive discounts multiply (20% + 10% ≠ 30%)

- Complete pricing chain: wholesaler → retailer → consumer

- Break-even discount = margin percentage

Master ratios and proportions for business analysis. This lecture covers ratio simplification, three notation forms, cross-multiplication, financial ratios (current, D/E, margin, turnover), proportional profit allocation, and unit rate comparisons.

What You Will Learn:

- What ratios are and how to simplify them

- Three ways to write ratios: colon, fraction, decimal

- Solving proportions by cross-multiplication

- Scaling production with proportional reasoning

- Four key financial ratios with benchmark ranges

- Complete ratio analysis of a company's financials

- Proportional profit allocation among partners (with pie chart)

- Unit rates for fair supplier comparison

Master the three most common percentage-based additions in business. This lecture covers sales tax across locations, tipping shortcuts, flat and tiered commission structures, combined scenarios, reverse calculations, and a complete paycheck example.

What You Will Learn:

- Sales tax formula and number line visualization

- Tax rates vary by location (NY, Oregon, CA, UK VAT comparison)

- Three tipping percentages with visual bar comparison

- The 15% tip shortcut (10% + half) applied to a real receipt

- Flat vs tiered commission structures

- Combined scenario: tax + commission + tip in one transaction

- Reverse calculations: finding pre-tax price from total

- Complete paycheck: base salary + commission − federal/state taxes = net pay

Master the simple interest formula I = PRT and all four rearrangements. This lecture covers savings deposits, short-term loans, day-count calculations, and investment comparisons using linear interest growth.

What You Will Learn:

- The I = PRT formula with four color-coded variables

- Step-by-step calculation with number line visualization

- Why simple interest grows in a straight line (linear)

- Four formula rearrangements to find I, P, R, or T

- Business loan with monthly time conversion (months ÷ 12)

- Day-count calculations (days ÷ 365) for commercial paper

- Comparing three investment options by total return

- Complete worked problem: finding the rate from repayment data

Discover why compound interest is called the eighth wonder of the world. This lecture covers the compound interest formula, simple vs compound comparison, compounding frequency, Rule of 72 verification, the power of starting early, effective annual rates, and mortgage implications.

What You Will Learn:

- The compound interest formula A = P(1 + R/N)^(NT)

- Step-by-step calculation vs simple interest comparison

- How the gap between simple and compound widens over time

- Effect of compounding frequency (annual to daily) with diminishing returns

- Rule of 72 verified with the compound interest formula

- Three investors starting at ages 25, 35, 45 — dramatic difference

- Effective Annual Rate (EAR) formula

- Mortgage compound interest: why total interest often exceeds the loan

Master the most important concept in finance: a dollar today is worth more than a dollar tomorrow. This lecture covers future value, present value, discount rate impact, NPV, IRR, and investment comparison.

What You Will Learn:

- The core insight: why money has a time dimension

- Future Value formula: FV = PV × (1+R)^T

- Present Value formula: PV = FV ÷ (1+R)^T

- Symmetric FV/PV curves around today

- How discount rate dramatically reduces present value

- Net Present Value (NPV) calculation step-by-step

- Internal Rate of Return (IRR) — rate where NPV = 0

- Side-by-side comparison of two investment projects

What You Will Learn:

- The monthly payment formula PMT = P(R/12) / (1−(1+R/12)^−N)

- Complete $20K car loan example: $386.66/month

- Total cost breakdown: principal vs interest (pie chart)

- 6-month amortization schedule table

- Principal vs interest crossover curve (month 36)

- Loan term comparison: 15 vs 20 vs 30 years

- Extra payment impact: save $49,700 and 6.3 years

- Refinancing decision analysis

Master the two most important metrics for evaluating business decisions. This lecture covers Return on Investment (ROI), annualized ROI, break-even units formula, the classic break-even chart, contribution margin, sensitivity analysis, and target profit.

What You Will Learn:

- ROI formula: Net Profit ÷ Investment × 100

- Positive, zero, and negative ROI scenarios

- Annualized ROI: time-adjusted returns

- Break-even units = Fixed ÷ (Price − Variable)

- The classic break-even chart (fixed, total cost, revenue lines)

- Contribution margin per unit and percentage

- Sensitivity analysis: how price, variable cost, and fixed cost affect BE

- Target profit formula

What You Will Learn:

- Mean formula and number line visualization

- Median: middle value of sorted data

- Mode: most frequent value (best for categorical data)

- Choosing the right measure based on outliers and data type

- Skewness: symmetric, right-skewed, left-skewed distributions

- Calculating all three for a 12-month sales dataset

- Weighted mean for student grades

- Business application: weighted margin across product lines

Measures of central tendency tell you the middle — measures of spread tell you the risk. Master range, variance, standard deviation, coefficient of variation, the empirical rule, and quality control applications.

What You Will Learn:

- Range (max − min) — simple but outlier-sensitive

- Variance formula and step-by-step calculation

- Standard deviation (σ) — the preferred business metric

- Portfolio risk: same expected return, very different volatility

- The 68-95-99.7 empirical rule for normal distributions

- Coefficient of variation (CV) — compare across scales

- How outliers inflate standard deviation

- Quality control with σ bands

Master the four essential business chart types and learn to design honest, clear visualizations. This lecture uses live-animated bar charts, tables, traced curves, and color-coded highlights for a polished visual experience.

What You Will Learn:

- Four chart types: bar, line, pie, scatter — when to use each

- Animated bar chart growth comparing Q4 sales by category

- Line charts revealing trends and seasonality (year-over-year comparison)

- Pie charts for composition (40% salaries, 25% materials, etc.)

- Scatter plots + best-fit lines for relationships (ad spend vs sales)

- Bad vs good chart design side-by-side

- When to use tables instead of charts (exact financial values)

- Three misleading traps: truncated axes, 3D distortion, cherry-picked ranges

Every business decision involves uncertainty — and probability is the mathematical framework for measuring that uncertainty precisely. In this lecture you will learn how to express probability in fractions, decimals, and percentages, apply the complement, AND, OR, and conditional probability rules, calculate expected value for any decision, and use these tools in quality control, financial scenario analysis, and decision tree thinking.

What You Will Learn:

- Express probability as a fraction, decimal, or percentage interchangeably

- Apply the complement rule: P(not A) = 1 − P(A)

- Use the AND rule for joint probability of independent events

- Apply the OR rule and subtract the overlap to avoid double-counting

- Calculate conditional probability when prior information changes the picture

- Compute expected value as the probability-weighted average of outcomes

- Apply probability formulas to quality control and defect rates

- Use decision trees to map multi-step uncertain choices

Business decisions almost always rely on samples rather than complete data — we cannot survey every customer or test every product. In this lecture you will learn how a small, well-designed sample can reveal patterns in millions of records, how the standard error measures estimation precision, why the Central Limit Theorem matters in practice, and how to attach confidence intervals to any estimate you produce.

What You Will Learn:

- Distinguish a population from a sample and why random sampling matters

- Calculate the standard error of the mean: SE = σ/√n

- Apply the Central Limit Theorem to use the normal distribution for inference

- Build a 95% confidence interval using the formula x̄ ± 1.96·SE

- Choose between 90%, 95%, and 99% confidence levels based on your goal

- Use the Student t-distribution when σ is unknown

- Plan sample size to achieve a desired margin of error

- Build confidence intervals for proportions in survey research

Every business runs on three numbers: revenue, cost, and profit. In this lecture you will learn how revenue equals price times quantity, how total cost decomposes into fixed and variable components, how contribution margin connects price to per-unit profit, and how break-even analysis defines the minimum viable volume. You will also explore gross margin, operating margin, and net margin — the three margin metrics that reveal a business model's quality at a glance.

What You Will Learn:

- Calculate revenue as price multiplied by quantity sold

- Decompose total cost into fixed and variable components

- Write the profit equation as Π = Q(P − v) − FC

- Calculate contribution margin per unit as price minus variable cost

- Find break-even quantity using fixed cost ÷ contribution margin

- Distinguish gross margin, operating margin, and net margin

- Understand operating leverage and how scaling amplifies profit

- Apply these formulas to evaluate any pricing or volume decision

Cost classification is the heart of managerial accounting. Every business expense falls into one of a few behavioral categories — and how those costs respond to volume changes determines pricing, planning, and forecasting accuracy. In this lecture you will learn the five cost behaviors, how to separate fixed and variable components from real-world data using the high-low method, and how to read cost curves to identify economies and diseconomies of scale.

What You Will Learn:

- Identify pure fixed costs and how per-unit fixed cost falls with volume

- Calculate pure variable costs that scale linearly with quantity produced

- Decompose mixed costs into fixed and variable components

- Recognize step costs that jump at activity thresholds

- Apply the high-low method to estimate cost equations from two data points

- Compare average cost vs marginal cost and find economies of scale

- Read cost curves at a glance — fixed, variable, mixed, and step

- Identify the optimal scale point on a U-shaped average cost curve

Cost-Volume-Profit analysis is the most-used framework in operational decision-making. It tells managers how profit responds to changes in price, variable cost, fixed cost, and sales volume. In this lecture you will master contribution margin, break-even in units and dollars, margin of safety, target profit analysis, and sensitivity analysis — the complete CVP toolkit for any pricing, volume, or cost decision.

What You Will Learn:

- Calculate contribution margin per unit (price minus variable cost)

- Compute the contribution margin ratio as a percentage of revenue

- Find total contribution margin = CM × quantity

- Calculate break-even in units: Fixed Cost ÷ CM per unit

- Calculate break-even in dollars: Fixed Cost ÷ CM ratio

- Measure margin of safety — your buffer against revenue shortfall

- Apply target profit analysis: convert profit goals into volume targets

- Read CVP graphs and run sensitivity analysis on any input

Long-lived assets machines, vehicles, buildings are not expensed at purchase. Instead the cost is spread across the asset's useful life via depreciation. In this lecture you will learn the three inputs that drive every depreciation calculation, the four primary methods used in financial accounting, the MACRS schedule used for US tax depreciation, and how to choose the right method for any asset and any business goal.

What You Will Learn:

- Identify cost, salvage value, and useful life  the three depreciation inputs

- Calculate depreciation using the straight-line method

- Apply the double-declining balance method to front-load depreciation

- Use the sum-of-years digits method for moderately accelerated depreciation

- Apply units of production to match depreciation to actual usage

- Read the 5-year MACRS schedule for US tax depreciation

- Compare all four methods on the same asset to see timing differences

- Choose the appropriate method based on wear pattern, reporting goals, and tax strategy

A budget is a financial plan expressed in numbers. It translates strategy into specific dollar amounts of revenue, expense, capital investment, and cash flow over a defined period. In this lecture you will learn how to build operating budgets, capital budgets, and cash flow forecasts, how to run variance analysis with flexible budgeting, and when to choose zero-based or rolling budgets over traditional incremental approaches.

What You Will Learn:

- Build an operating budget line by line from revenue down to net profit

- Triangulate revenue forecasts using historical, bottom-up, and top-down methods

- Plan capital expenditures using NPV and payback criteria

- Build a 13-week and 12-month cash flow forecast

- Run variance analysis: actual vs budget with price, volume, and mix decomposition

- Apply flexible budgeting to isolate volume effects from spending efficiency

- Use zero-based budgeting to reset accumulated assumptions

- Implement rolling budgets that always look 12 months forward

Inventory is one of the largest assets on most retailer and manufacturer balance sheets. How you value inventory affects cost of goods sold, gross profit, taxable income, and the inventory line on the balance sheet itself. In this lecture you will learn the periodic and perpetual tracking systems and the four valuation methods, with worked examples comparing how each method changes profit and tax outcomes.

What You Will Learn:

- Distinguish periodic and perpetual inventory systems

- Apply FIFO (First In, First Out) oldest inventory sells first

- Apply LIFO (Last In, First Out) newest inventory sells first

- Calculate weighted average cost per unit

- Apply specific identification for high-value, distinguishable items

- Compare all four methods on identical purchase data

- Understand inflationary effects on COGS, profit, and ending inventory

- Choose the right method based on your tax, reporting, and physical-flow goals

Every business that holds inventory faces a tension: order in large quantities to save on ordering costs, or order in small quantities to save on storage. The EOQ formula is the mathematical answer that minimizes total inventory cost. In this lecture you will derive the EOQ formula from first principles, work through a complete numerical example, and learn how to handle quantity discounts, safety stock, and reorder points in real-world inventory management.

What You Will Learn:

- Identify the three cost inputs: demand, order cost, holding cost

- Apply the EOQ formula: Q* = √(2DS/H)

- Decompose total annual cost into ordering and holding components

- Visualize the U-shaped total cost curve and find its minimum

- Use the shallow EOQ curve to round to operationally convenient quantities

- Adjust EOQ for quantity discounts at supplier price tiers

- Calculate safety stock for variable demand and lead times

- Determine reorder points: ROP = (daily demand × lead time) + safety stock

- Measure inventory turnover and benchmark against industry norms

Payroll is more than just hours times rate. Every paycheck involves gross pay, mandatory tax withholding, voluntary deductions, employer-side payroll taxes, and net pay delivered to the employee. In this lecture you will walk through the complete payroll calculation flow, from gross pay all the way through to total cost of employment for the company.

What You Will Learn:

- Calculate gross pay for hourly, salaried, overtime, and bonus pay

- Apply progressive federal income tax brackets via the W-4 system

- Calculate FICA (Social Security 6.2% + Medicare 1.45% = 7.65%)

- Distinguish state and local income tax variation across jurisdictions

- Distinguish pre-tax vs post-tax deductions and their tax savings

- Compute net pay through the complete deduction sequence

- Calculate employer-side taxes: FICA match, FUTA, SUTA, workers comp

- Determine total cost of employment including benefits and taxes

After 27 lectures of business mathematics, this lecture connects everything into one integrated framework. You will see how foundations, time value of money, statistics, operations, accounting, and capital decisions interconnect into a single coherent toolkit. By the end you will recognize when to deploy each tool, how the tools relate to each other, and where your strongest and weakest areas are before the case study and finale.

What You Will Learn:

- Map all 27 prior lectures into seven major topic areas

- Recognize the foundational vocabulary that appears across every section

- Connect time value of money to investment, loan, and retirement decisions

- See how statistics underpins every business projection

- Connect revenue, cost, and profit to operational daily decisions

- Tie depreciation, inventory, and payroll to financial reporting

- Link NPV-based capital decisions to EOQ-based operational decisions

- Identify the common thread: quantitative discipline replaces guessing

In this capstone case study, you will apply every tool from the course to one integrated decision. Sarah, a coffee shop owner, is considering opening a second location requiring $150,000 in upfront investment. You will walk through revenue forecasting, cost classification, profit projection, break-even analysis, capital budget, NPV, and sensitivity analysis to reach a defensible quantitative recommendation.

What You Will Learn:

- Triangulate revenue projections using three estimation methods

- Classify operating costs as fixed and variable percentages of revenue

- Project annual operating profit and operating margin

- Calculate break-even revenue and margin of safety

- Plan total capital investment including build-out, equipment, and working capital

- Compute payback period and net present value at a 10% discount rate

- Run sensitivity analysis on revenue, cost, and combined adverse scenarios

- Reach a defensible go/no-go decision backed by quantitative evidence

In this final lecture you will consolidate the complete business math toolkit, identify the most important takeaways, and chart a path for continued mastery. You will learn which concept is the most powerful single insight in finance, which technique is the most important practical habit, how to use spreadsheets to multiply your effectiveness, and which advanced fields naturally extend the foundation you have just built.

What You Will Learn:

- Recap the seven major topic areas from the course

- Identify the most powerful single concept: the time value of money

- Identify the most powerful single technique: sensitivity analysis

- Build practice habits to convert knowledge into lasting skill

- Use Excel and Google Sheets financial functions (NPV, IRR, PMT, PV, FV)

- Map next learning steps: financial accounting, corporate finance, data science

- Discover essential books and free online resources for continued learning

- Establish lifelong habits that compound your quantitative intuition