The Decision Matrix — Rent vs. Buy, Debt vs. Invest

The answer to "rent or buy?" and "pay off debt or invest?" depends on eleven variables — and in both cases, the most important one is the opportunity cost of money sitting in something other than a market portfolio.

Two of the largest decisions a household makes in its accumulation years are whether to buy a house and whether to accelerate its debt payoff. They look like different problems — one is about real estate, the other about interest arbitrage — but the math underneath is the same. You're comparing two paths for a pile of money and asking which produces more wealth at some horizon. The pile, the return assumption, and the horizon are the three variables that actually matter. The rest are decorations.

Rent vs. Buy: the only formula that matters

Net wealth at horizon T from buying is your equity (home value minus mortgage balance) minus transaction costs to sell, plus any savings you also accumulated. Net wealth from renting is whatever your down-payment-and-monthly-difference pile grew to in a market portfolio. Whichever number is bigger wins. That's it.

net_buy(T)  = home_value(T) − mortgage_balance(T) − sell_costs + savings_buy(T)
net_rent(T) = invested_difference(T) + invested_down_payment(T)

Plug your real numbers into the Rent vs. Buy tab in the sandbox and the chart shows both terminal-wealth lines side by side. The crossover year — where the buying line passes the renting line — is your personal break-even horizon. For most metros that crossover lives somewhere between year seven and year ten; below that horizon, the transaction costs and the lost compounding on the down payment usually mean renting wins.

The hidden variables nobody models

Most rent-vs-buy comparisons leave out the carrying costs that actually matter, which is why they reach the wrong answer. Three variables in particular are systematically under-modeled.

Maintenance is real. One to two percent of home value per year, every year. A $500,000 house consumes $7,500 a year just to not fall apart. New construction trends to the low end; anything past twenty years old trends past 2% once you start amortizing roof, HVAC, and major-system replacement. Almost every spreadsheet comparison either omits this entirely or budgets a tenth of what it actually costs.

Transaction costs are 6% on exit. Realtor commission, title, closing fees, transfer taxes. If you sell in year five, you just gave away most of your home's appreciation. This is why the break-even horizon is years, not months — you need enough appreciation to outrun the haircut on the way out.

Opportunity cost is the silent biggest. A $100,000 down payment that sits in home equity for ten years earned you the appreciation of your house. The same $100,000 in a market portfolio earned compound returns at 7% — roughly $97,000 in additional wealth on top of the original principal. Whether buying wins depends on whether your house outran that.

Debt vs. Invest: the same problem, dressed differently

Switch to the second tab. Same opportunity-cost question, different framing. You have an extra $500 per month and a debt at some interest rate. Pay it down faster or invest? The decision rule is roughly: choose pay-down when the after-tax debt rate (adjusted for the certainty premium — risk-free returns are worth more than risky ones) exceeds the expected after-tax investment return.

In practice that means: high-interest debt (credit cards, anything above ~7–8% after taxes) is almost always pay-down. Mid-range debt (5–7%) is a coin flip that tips on your tax bracket and risk tolerance. Low-rate debt (under 4–5%, like most 2020–2021 mortgages) is almost always invest, because the after-tax cost of the debt is below long-run market expectations.

The sandbox lets you slide the debt rate and the expected return independently and watch the winner flip. Notice how the crossover happens around 5% for typical risk preferences — that's not a coincidence, it's roughly where the certainty premium balances the equity risk premium for most people.

Refinance: a special case

Refinancing is just debt-vs-invest with two debts to compare. If your current rate is 6.5% and refinancing offers 5.5% with $4,000 in closing costs, the break-even is closing-costs divided by annual savings — usually around 3 years for a 1% rate drop. The 0.5% rule-of-thumb you'll see online is too aggressive; closing costs usually take 5+ years to recover at that drop. The standalone Mortgage Refinance Calculator handles the full break-even and lifetime savings calculation.

What to do today

Three concrete actions.

1. Estimate your real holding horizon. Not what you'd like to be true. What's actually true. If you're a renter considering buying, look at the last decade of your life and ask whether you've stayed in any one apartment for ten years. The rent-vs-buy decision is sensitive to this number; almost nothing else swings the answer as much.

2. Budget for maintenance, on paper. If you already own a house, set up a sinking fund (Smart Jar) at 1.5% of home value per year. If you don't, knowing this number changes the model. The Smart Budgeting page covers the mechanics.

3. Run the alternative. The most common reason people regret a house purchase isn't the house — it's that they never modeled the alternative. Spend ten minutes in the sandbox to the right with your real numbers, then make the call. The cost of modeling is much smaller than the cost of being wrong.

Where to go from here

Calculators model decisions in isolation; the full simulator models them together — and the interaction matters. Buying a house affects your savings rate, which affects your investment growth, which affects when you cross FI, which affects when Roth conversions become possible. The Compounding Engine covers the savings-rate side; the Coast FIRE Checkpoint covers the moment your accumulated portfolio takes over from active saving. Both feed back into this decision.