The math of money: loans, interest, taxes and retirement, step by step
Every number on a loan statement, savings account or tax table comes from a formula you can compute yourself. Here are the formulas, with the steps and the sources, and no advice about what to do with your money.
8 pages in this section
- GuideLoan payment formula, step by stepThe fixed monthly loan payment formula, a calculator, where it comes from, worked examples and common mistakes.
- GuideAPR vs APY: The Difference, With the Math and ExamplesAPR is the yearly rate before compounding; APY is the rate after it. See the formula, 5% and 24% examples, a calculator and how loan fees change APR.
- GuideCompound Interest Formula: Examples and CalculatorThe compound interest formula A = P(1 + r/n)^(nt) with a calculator, worked examples, solving for rate and time, APY and the Rule of 72.
- GuideHow Much Do You Need to Retire? The Math, Step by StepA retirement number is one division: yearly spending minus Social Security, over a withdrawal rate. Worked examples, 2026 limits and a calculator.
- GuideHow Long to Pay Off a Loan: Formula and CalculatorWork out how many months a loan takes to pay off with the loan-term formula, a calculator, worked examples and what extra payments change.
- ReferenceHow US Income Tax Brackets Work: 2026 Rates and ExamplesEach bracket taxes only the slice of income inside it. IRS 2026 and 2025 tables for every filing status, a $100,000 example and a calculator.
- GuideRent vs Buy Math: The Formula and a Worked ExampleCompare renting and buying with one budget: payment formula, unrecoverable costs, break-even year, the 5%, 2% and 30% rules and a calculator.
- GuideThe Rule of 72 Explained: How Fast Money DoublesDivide 72 by the yearly rate to estimate how long money takes to double. The formula, worked examples, a calculator, an accuracy table and why 72.