📄️ Future-Value Formula
Master the future value formula—the core equation that projects how your money grows. Learn the variables, interpret the exponent, and apply it to real scenarios.
📄️ Present-Value Formula
Understand present value—the inverse of future value. Discount future money to today's dollars. Essential for comparing investment options and making rational financial decisions.
📄️ FV With Annual Contributions
Calculate future value when adding regular money each year. Master the annuity formula with detailed worked examples for savings, retirement, and investment planning.
📄️ FV With Monthly Contributions
Calculate future value with monthly savings or investment deposits. Master the real-world formula used by most people's actual savings patterns and retirement accounts.
📄️ Solving for Rate
Learn to solve compound interest equations for the interest rate—essential for evaluating investments and comparing returns. Includes approximation methods and worked examples.
📄️ Solving for Time
Learn to solve compound interest for time using logarithms. Master the formula to calculate how many years your investment needs to double or reach a target.
📄️ Continuous Compounding
Explore continuous compounding and the mathematical constant e. Learn why the most frequent compounding possible creates a clean formula and connects to exponential growth.
📄️ CAGR Explained
Master CAGR (Compound Annual Growth Rate) with worked examples. Learn how to calculate year-over-year growth, compare investments fairly, and avoid common pitfalls.
📄️ CAGR vs Average Return
Understand the critical difference between CAGR and average return. Learn when each metric matters and how volatility creates the gap between them.
📄️ IRR for Beginners
Learn IRR (Internal Rate of Return) from first principles. Understand cash flows, discounting, and how IRR differs from CAGR in practical investment analysis.
📄️ Time-Weighted vs Money-Weighted
Master time-weighted and money-weighted returns. Learn why they differ when you add or withdraw cash, and which metric your advisor should use.
📄️ Real vs Nominal Return
Discover why your 7% stock market return feels like 4% in your wallet. Learn real vs nominal returns and how inflation silently erodes your wealth.
📄️ Compounding With Cash Flows
Master compounding when money flows in and out. Learn how deposits, withdrawals, and timing amplify or suppress your wealth growth over decades.
📄️ Compounding Frequencies
Compare daily vs monthly vs annual compounding. Learn why compounding frequency matters and how it reshapes your returns over decades.
📄️ APR vs APY
Master APR vs APY. Learn why credit card companies promote APR while banks advertise APY, and how the difference costs you thousands.
📄️ Effective Annual Rate
Compare investments fairly by calculating effective annual rate. Learn how different compounding frequencies disguise true returns and work through real examples.
📄️ Natural Log and Compounding
Understand why the natural logarithm (ln) simplifies compound interest calculations. Learn how e, ln, and exponential functions connect and solve real problems.
📄️ Compound Formula in Spreadsheet
Translate compound interest formulas into Excel, Google Sheets, and other spreadsheets. Build models, use named ranges, and automate calculations.
📄️ Percentage Points vs Percent Change
Distinguish between percentage points and percent change—a critical distinction that prevents misreading financial statements and news headlines.
📄️ Rounding Errors in Compound Math
Understand how rounding at each step accumulates in compound calculations. Learn when to round, when to carry decimals, and how to verify your work.