Plain Money Math

Articles

Every piece works through the arithmetic and lists the primary sources it was checked against.

Retirement

Roth vs Traditional Is One Question, Not Two
If your tax rate never changes, the two accounts produce exactly the same money. Once you see why, the decision reduces to a single question about your future rate.
2026-08-31 · 3 min read

Investing

Total-Market Funds and S&P 500 Funds: The Actual Difference
One holds a few hundred large companies, the other holds thousands. In practice they behave more alike than that suggests, and the reason explains most of what people get wrong about diversification.
2026-08-30 · 3 min read
How Many Funds a Portfolio Actually Needs
Adding a fifth fund usually changes a portfolio less than people expect. The reason is structural, and you can check it on your own holdings in about two 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 investment horizon arrives at the end. Understanding why explains both why starting early matters and why the early years feel like nothing is happening.
2026-08-26 · 3 min read

Credit Cards

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. Here is the arithmetic, and the three places it usually goes wrong.
2026-08-28 · 3 min read