— Long-form
Guides and explainers on the ideas behind the calculators — saving, investing, borrowing, retirement and valuation, worked through in plain English.
Valuation
A founder told their company is "worth $20 million" walks home feeling like they own a $20 million asset. They do not. The number is a negotiated price for a financial instrument — not a measurement of worth — and confusing the two quietly costs founders real ownership.
Loans
A small monthly payment feels like control. The math says otherwise. Here is how credit cards, minimum payments and compounding interest quietly turn a manageable balance into a multi-year, multiples-of-principal liability — and the strategies that get you out.
Budgeting
Everyone repeats "save three to six months of expenses," but almost nobody can tell you where the range came from, or why it should be identical for a tenured professor and a commission-only salesperson with three kids and a mortgage. Here is how to derive your number from the risks you actually carry — and to count the cost of getting it wrong in either direction.
Retirement
Ask most people for their "FIRE number" and they quote a single figure. But there isn't one number — there are four, and they are four genuinely different math problems, each quietly changing a different term in the same equation. Here is the equation behind each, so "which one is mine?" stops being a vibe and becomes arithmetic.
Retirement
Bengen's 1994 paper is famous; the arithmetic inside it is not. The four was never the typical answer — it was the worst answer in the worst case in the worst decade of modern American financial history. We rebuilt the spreadsheet from scratch to show what actually falls out.
Budgeting
Cash flow, budgeting, savings rate, the emergency fund and net worth are usually taught as five separate chores. They are not — they are five layers of one machine, each driving the next. Here is how the whole system fits together, and how to actually run it on about thirty minutes a month.
Retirement
Two people save the same amount, earn the same average return, and withdraw the same income. One dies with millions; the other runs out before their seventieth birthday. The only thing that separated them was the order in which their returns arrived. This is sequence-of-returns risk — the quiet machinery underneath the famous 4% rule.
Investment
Einstein probably never said it, but the underlying math has been the most-broken promise of personal finance for a hundred years.
Mortgage
"Renting is throwing money away" is the most expensive myth in personal finance. The honest comparison turns on opportunity cost, transaction fees, and how long you actually stay put.
Valuation
Discounted cash flow is the most teachable valuation method and one of the easiest to manipulate.
USD / EUR
0.8655 ▼ 0.34%
S&P 500
7,609 ▲ 0.18%
Gold ($/oz)
4,487 ▼ 0.01%
Crude ($/bbl)
93.31 ▲ 0.88%