At Six Per Cent, a Promise Thirty Years Out Is Worth a Sixth

The rule of 72 works here too, backwards

Divide 72 by the rate and you get the number of years for a sum to double — or, read the other way, for a future sum to be worth half. At 6 % the rule predicts 12 years, and the exact figure is 11.9; the calculator gives a factor of 0.497 at twelve years, which is a hair under a half. The approximation is good between about 4 % and 12 % and drifts outside that band, but its real value is that it turns a table lookup into mental arithmetic. Anyone quoting you a long-dated payout can be checked in a second: at 8 %, halving every nine years, a promise twenty-seven years out is worth an eighth of its face.

Why the choice of rate is an argument, not a fact

The gap between 3 % and 6 % over thirty years is the difference between valuing a commitment at $412 and at $174. That is why the rate is contested wherever long horizons meet public money: the same climate policy, the same pension liability or the same infrastructure project can be shown as worthwhile or wasteful depending on a figure that reflects a judgement about how much the distant future counts. The arithmetic is neutral and the input is not. When a report leads with a present value, the first useful question is always which rate produced it and who chose that rate.

Frequently asked questions

Should the rate include inflation?

Only if the cash flows do. The rule is to be consistent: discount nominal amounts with a nominal rate, or amounts expressed in today's money with a real rate that excludes inflation. Mixing them is the most common error in an otherwise careful model, and it is a large one — three points of inflation over thirty years changes the answer by a factor of nearly two and a half, exactly as the table shows. The safest habit is to state on the model itself which convention is in use, because a spreadsheet inherited from a colleague rarely says.

Does the factor ever reach zero?

Never exactly, but it gets there for practical purposes. At 6 % a payment a hundred years out is worth 0.29 % of its face value, and one two hundred years out is worth 0.0009 %. This is why perpetual formulas converge at all: an infinite stream of payments has a finite present value, because the terms shrink geometrically. It is also why very long-dated obligations are difficult to argue about with this tool — the arithmetic says a harm in three centuries is worth almost nothing today, which is a conclusion about the formula rather than about the harm.