Chapter 2
The Mathematics of Money
Every chapter after this one leans on the same small toolbox. One force — inflation, which compounds against you. One engine — compound growth, which compounds for you. And a handful of operations built on the pair: deflating dollars across time, discounting future cash back to the present, pricing streams of payments, and deciding what a return must clear before it counts as a return at all. None of it is harder than high-school algebra, and all of it is load-bearing: the retirement number, the mortgage decision, and the valuation of every asset in this book reduce to these few moves. Learn them once, here, and every later chapter gets shorter.
Inflation: The Silent Tax
Inflation over Several Years
Real Income
Which Number to Plan With
Interest Rates and the Fed
Compound Interest
The Second Eroder: Tax on the Compounding Itself
Rule of 72
Compound Annual Growth Rate (CAGR)
Present vs. Future Value
Loan Amortization (Annuities)
Perpetuity
Discounted Cash Flow and Net Present Value
Internal Rate of Return (IRR)
Estimating Retirement Needs
Sequence of Returns Risk
Safe Withdrawal Rate — Why 4%?
Calculating Savings Rate
Savings Rate For Retirement
Lifestyle Inflation: The Hedonic Treadmill
Financial Flexibility
Cash and Current Ratios
Debt-to-Total-Assets Ratio (D/TA)
Days Not Working
Expected Value, and When to Ignore It
Opportunity Cost: The Hidden Price Tag of Every Decision
Financial Leverage
The Arithmetic of Leverage
Stress the Assumptions, Not the Arithmetic
Inflation over Several Years
Real Income
Which Number to Plan With
Interest Rates and the Fed
Compound Interest
The Second Eroder: Tax on the Compounding Itself
Rule of 72
Compound Annual Growth Rate (CAGR)
Present vs. Future Value
Loan Amortization (Annuities)
Perpetuity
Discounted Cash Flow and Net Present Value
Internal Rate of Return (IRR)
Estimating Retirement Needs
Sequence of Returns Risk
Safe Withdrawal Rate — Why 4%?
Calculating Savings Rate
Savings Rate For Retirement
Lifestyle Inflation: The Hedonic Treadmill
Financial Flexibility
Cash and Current Ratios
Debt-to-Total-Assets Ratio (D/TA)
Days Not Working
Expected Value, and When to Ignore It
Opportunity Cost: The Hidden Price Tag of Every Decision
Financial Leverage
The Arithmetic of Leverage
Stress the Assumptions, Not the Arithmetic