Present Value vs Future Value: Why Money in Thirty Years Is Worth About an Eighth of Its Face

One equation, read in two directions

Future value compounds: put $10,000 in at 7 percent and after thirty years it is $76,123, because each year's interest joins the base that earns the next year's. Present value undoes exactly that: $76,123 thirty years out, discounted at 7 percent, is $10,000 today. Nothing new is introduced going backwards — you divide by the same (1+r)^n you multiplied by. The two are inverse operations on the same growth factor, which is why any present-value question can be checked by compounding the answer forward and seeing whether you land on the original amount.

The useful habit is to think in discount factors rather than in amounts. The factor 1 ÷ (1+r)^n depends only on the rate and the horizon, never on the sum, so one table answers every question at that rate. Reading across the 7 percent row of the table above: a unit of money is worth 0.935 next year, half its face at ten years, a quarter at twenty and an eighth at thirty. Multiply any future amount by the factor and you have its present value; that is all discounting is. It also makes the arithmetic auditable, because a factor greater than one or a factor that rises with the horizon is a mistake you can see immediately.

The tail of a long projection is worth almost nothing

At 7 percent, a present value halves roughly every 10.2 years, because 1.07 to the power 10.2 is 2. That is the fact that makes long-horizon promises so much weaker than they look. A pension statement quoting $100,000 at retirement in thirty years is quoting $13,137 in today's terms. A guarantee that pays out in year 25 is worth less than a fifth of one paying out today. And a business case whose returns arrive after year 20 is, at a 7 percent rate, barely a business case at all — the discount factor has already eaten three quarters of the value before the first cash flow lands.

The same effect appears inside any stream of payments. Discount $1,000 a year for thirty years at 7 percent and the whole stream is worth $12,409 today — twelve times the annual figure, not thirty. Split that value by decade and the first ten years supply 56.6 percent of it, the second ten 28.8 percent, and the last ten only 14.6 percent. This is why a thirty-year forecast is usually no more informative than a twenty-year one, and why arguing over year-28 assumptions is nearly always a waste of a meeting. It is also the honest defence of terminal values in valuation work: they exist precisely because the far tail cannot be forecast and does not need to be, only bounded.

Which is why the discount rate is the most contested number in any valuation

Everything above assumed a rate. Change only that, and the answer moves further than any other input could move it. A promise of $100,000 in thirty years is worth $41,199 at 3 percent, $23,138 at 5 percent, $13,137 at 7 percent and $5,731 at 10 percent. The gap between the first and the last is a factor of 7.2 — from an assumption that cannot be measured, only argued for. Nobody negotiating a settlement, a pension transfer value or an infrastructure appraisal is really arguing about the arithmetic; they are arguing about r, because whoever picks r has already picked the answer.

This is why serious institutions prescribe the rate rather than leaving it to the analyst. The US Office of Management and Budget publishes discount rates that federal benefit-cost analyses must use, and HM Treasury's Green Book sets a declining schedule of social discount rates for UK appraisals precisely so that long-horizon projects are not killed or resurrected by an author's choice of r. Whatever you are valuing, the discipline is the same: state the rate, state why, and show the answer at two or three other rates as well. A present value quoted without its rate is not an answer, it is an assertion.

Frequently asked questions

What discount rate should I use?

The rate should reflect what the money would otherwise earn at comparable risk. For your own decisions, that is usually the return on the safest thing you would actually do with the cash — paying down a loan, or a deposit account — after tax. For a company appraising a project, it is the weighted average cost of capital. For a public body, it is whatever the national guidance prescribes. What matters more than the number is that it is the same across every option you compare and that you show the answer under at least one alternative rate, because that is what reveals how fragile the conclusion is.

Should the rate be nominal or real?

Match it to the cash flows. Nominal flows — amounts as they will actually be paid, inflation included — need a nominal rate. Real flows, expressed in today's purchasing power, need a real rate, which is (1+nominal) ÷ (1+inflation) − 1, not the subtraction most people do: 7 percent nominal with 2 percent inflation is a 4.90 percent real rate, not 5 percent. Mixing the two is the single most common error in long appraisals, and it is not small. Discount a nominal $100,000 thirty years out at that 4.90 percent real rate and you get $23,795 instead of $13,137 — 81 percent too high, because you have quietly removed thirty years of inflation twice over.

Is present value the same thing as net present value?

Almost. Present value discounts a future amount, or a stream of them, back to today. Net present value does the same and then subtracts what you have to pay to get them, so it nets the inflows against the outflows. The present value of $20,000 a year for ten years at 8 percent is $134,202; if acquiring that stream costs $100,000 today, the net present value is $34,202. The word net is doing real work — it is the difference between what something is worth and whether it is worth buying.