Guides
The math card companies count on you not doing
How interest grows, why a dollar today beats a dollar later, and how to measure what your money really earns. Every guide has a calculator and shows its work.
Interest basics
Simple interest, compound interest and how fast money doubles.
- Simple vs compound interest, and how interest becomes returnSimple vs compound interest with formulas and side-by-side numbers, APR vs APY, where each one shows up on loans and cards, and how interest relates to return.8 min read →
- How compound interest works, and why starting early winsHow compound interest works, the formula A = P(1 + r/n)^(nt), growth with monthly contributions, the cost of waiting, and a free compound interest calculator.8 min read →
- The rule of 72: how fast your money doublesDivide 72 by your rate to see how many years money takes to double. How the rule of 72 works, how accurate it is, and what it says about inflation and debt.9 min read →
Time value of money
Why a dollar today is worth more than a dollar later, and the formulas that price it.
- The time value of money, explained simplyWhy a dollar today is worth more than a dollar later, the two formulas behind it, worked examples, and a free time value of money calculator.7 min read →
- The time value of money formula, step by stepEvery time value of money formula: future and present value, annuities, perpetuities, solving for rate or years, with worked examples and Excel functions.9 min read →
- Present value: what future money is worth todayWhat present value means, the PV formula, how to pick a discount rate, net present value, and a calculator for a lump sum versus payments, with examples.8 min read →
Rate of return
How to measure what your money earns, average it honestly, and keep more of it.
- How to calculate rate of returnThe rate of return formula with dividends included, ROI, holding period return and CAGR, worked examples, the Excel RRI function and a free calculator.8 min read →
- Average return vs annualized returnWhy the average of yearly returns is higher than what your money earned, how to calculate both, volatility drag, and the S&P 500 example with real data.8 min read →
- Time-weighted vs money-weighted return: your return when you keep adding moneyHow to calculate your return when you add or withdraw money: time-weighted vs money-weighted return, XIRR in Excel and Google Sheets, and Modified Dietz.8 min read →
- What rate of return should you expect on investments?What stocks, bonds and cash have actually returned since 1928, how much returns swing, and how to pick a realistic rate of return for your plan.8 min read →
- Real rate of return: what you earn after inflationHow to calculate the real rate of return after inflation, why nominal minus inflation is only a shortcut, and what stocks and savings earned in real terms.8 min read →
- Investment fees: how fees and small rate differences cost youWhat a 1% fee really costs over 30 years, how expense ratios and advisory fees compound, and the parts of your rate of return you can actually control.9 min read →