What is a future euro worth today?
Reverse the compounding machine and you get the tool professionals use more than any other: discounting — the market's way of pricing promises.
Running the machine backwards
If €1,000 today grows to €1,050 in a year at 5%, then a rock-solid promise of €1,050 one year away is worth exactly €1,000 today. Not less, not more — because €1,000 is what you'd need today to reproduce that future amount yourself. The promise's present value (PV) is the future amount shrunk back by the rate:
PV = future amount ÷ (1 + rate)^years.
A promise of €1,000 in 10 years, discounted at 5%: about €614 today. At 10%: about €386. Same promise — wildly different present values, depending on one input.
The rate is the volume knob
Notice what just happened: the higher the discount rate, the less any future money is worth today. This single line explains most of the macro course's gravity: stocks are claims on future profits, bonds are schedules of future coupons — ALL of it is discounted future money. When rates rise, the discounting gets harsher, and every price built on tomorrows falls, mechanically. Long-dated Treasuries are the purest case, because almost all of their money is far away and therefore heavily discounted — here is the fund that holds them, over five years:
The 2022 stretch of that line is this formula doing its work at scale.
Risk raises the knob too
A government's promise and a startup's promise of the same €1,000 do not discount at the same rate — the shakier promise gets a higher rate (the risk rent), hence a lower present value. That, in one sentence, is why risky assets must offer higher potential returns to find buyers at all: the market charges promises for their doubt.
Try it now
- Compute (rough mental math welcome): PV of €2,000 in one year at 5%? Around €1,905 — check yourself against the formula.
- Explain in two sentences why rising rates mechanically lower the present value of a stock's future profits. Then find 2022 on the chart above, and check the explanation against what actually happened to the price of the longest-dated promises in the market.
- Two promises of €1,000 in 5 years — one from a trusted government, one from a young startup. Which has the higher present value, and which rent explains the gap?