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Compound interest is just earning returns on returns. The math is simple. The reason it's powerful — and the reason most people get it wrong — is that the curve barely moves for the first 10 years.

Vanguard's research and our Monte Carlo runs converge on the same answer: lump sum wins about two-thirds of the time. The interesting question is what happens in the third where DCA wins, and whether you'd survive it.

The 25× rule survives 30-year retirements 95% of the time. Stretch the horizon to 45 years and survival drops to 76%. Here's why early retirement needs a different multiplier — and what fixes it without saving more.

A rent-vs-buy calculator that only compares mortgage to rent is missing 60% of the math. Here are the seven lines that move the break-even year by 3-7 years when included honestly.

First salary becomes the base every percentage raise multiplies. We ran the same $5K negotiation at ages 25, 35, and 45 — the 25-year-old gets 8× the lifetime impact for the same conversation.

PSLF halves the IDR forgiveness timeline to 10 years and, unlike standard IDR forgiveness, is completely tax-free under IRC §108(f)(4). We ran the numbers on a typical public-school teacher's balance.

An $80,000 forgiveness can land a borrower in the 24% federal bracket, owing roughly $19,000 to the IRS in a year they hadn't budgeted for. We walked through why the 'bargain' has a bill attached.

BLS data shows the headline lifetime earnings premium. Georgetown's Center on Education and the Workforce shows the honest reading underneath: engineering and CS majors clear $80K+ lifetime medians while some other majors net less than skilled trades.

Legal fees range from a few thousand dollars to $50,000+ in a contested case, and they get all the attention. Splitting one household into two typically multiplies living costs by 1.5-1.6x — a structural cost that compounds for years.

Moving in together doesn't halve costs or double them. The OECD's square-root equivalence scale says a two-person household needs about 1.41x a single person's budget — we ran what that frees up.

The second earner's paycheck stacks on top of the first at the household's marginal rate, then childcare takes another $12,000-$24,000+ per child. We checked exactly where the math flips positive.

The feared marriage tax penalty barely exists for most couples. We checked the 2025 federal brackets and found the more common outcome is actually a bonus — and it gets bigger the more incomes differ.

Equal dollars aren't equal impact. We ran the numbers on a couple earning $8,000 and $2,000 a month splitting $3,000 in shared bills — and checked what a proportional split does instead.

The arithmetic is straightforward but most people don't internalize it until they see the chart. We ran the compounding math behind the core argument for low-cost index investing.

The classic rule was written for stable salaried workers in single-income households. A dual-earner tech couple and a solo gig worker with kids face completely different risk profiles with the same number.