Articles
Every piece works through the arithmetic and lists the primary sources it was checked against.
Debt
Investing
Why the First $100,000 Is the Slowest
The first milestone takes years. The tenth takes months. Same contribution, same return — only the balance doing the earning changed.
2026-09-11 · 4 min read
How Much Belongs in Stocks Is Not a Question About Age
The familiar rules of thumb disagree by twenty points at the same age. What decides it is how long you could avoid selling.
2026-09-02 · 3 min read
Gold Earns Nothing, and That Is the Whole Argument
An ounce of gold today is an ounce in thirty years. Every dollar of return has to come from someone paying more later.
2026-09-01 · 4 min read
What an Active Trader Actually Has to Overcome
Give a trader and a holder identical returns, then add costs and tax. See how big an edge is needed just to draw level.
2026-08-31 · 5 min read
What a Bond Actually Is, and Why Its Price Falls When Rates Rise
A bond's payments never change. Only what the market demands does, and that alone moves the price. The arithmetic behind it.
2026-08-31 · 3 min read
Total-Market Funds and S&P 500 Funds: The Actual Difference
One holds a few hundred large companies, the other thousands. In practice they behave far more alike than that suggests.
2026-08-30 · 3 min read
A Dividend Is Not Free Money
When a dividend is paid, the share price drops by the same amount. Why that changes how you read every yield figure.
2026-08-30 · 3 min read
How Many Funds a Portfolio Actually Needs
Adding a fifth fund changes a portfolio less than people expect. The reason is structural, and you can check it in minutes.
2026-08-29 · 3 min read
Compounding Is Back-Loaded, and That Changes What You Should Worry About
Most of the growth in a long horizon arrives at the end. Why that makes the early years feel like nothing is happening.
2026-08-26 · 5 min read
Retirement
The Order You Withdraw From Changes the Total
Same accounts, same spending, same returns. Which one you drain first moves the ending balance by more than most people would guess.
2026-09-07 · 4 min read
The Point Where Saving Becomes Optional
Long before you can retire, there is a balance that reaches your target on its own. It arrives earlier than people expect.
2026-09-01 · 4 min read
Roth vs Traditional Is One Question, Not Two
If your tax rate never changes, the two accounts produce exactly the same money. That reduces the decision to one question.
2026-08-31 · 3 min read
The Retirement Risk That Averages Hide
Two retirees can earn identical average returns and end up in very different places. The order the returns arrived in decides it.
2026-08-30 · 3 min read
Your Employer Match Is Not a Bonus, It Is Part of Your Pay
A match you do not collect is a pay cut you agreed to. How the formula works and what it is worth over a career.
2026-08-29 · 3 min read
Cashing Out a Retirement Account Costs Twice
Tax and penalty are the visible cost. The compounding you gave up is usually larger, and it never shows on a statement.
2026-08-29 · 4 min read
Credit Cards
The Minimum Payment Is the Trap
It falls as your balance falls, so the payoff date moves away as you approach it. Freezing it costs nothing extra this month.
2026-09-01 · 5 min read
What a Credit Card Annual Fee Actually Has to Earn Back
An annual fee is not a cost or a bargain on its own. It is a break-even problem, and here is the arithmetic that settles it.
2026-08-28 · 3 min read
Housing