Quick: €1,000 grows at 6% a year for 40 years. How much do you end up with?
Most people say something around €3,000 or €3,500. The real answer is about €10,300, three times more. This first hands-on tutorial follows the Wealth Principles series and explains why that guess goes so wrong, and how to do the maths yourself.
The problem: we think in straight lines
Economists Victor Stango and Jonathan Zinman call it exponential growth bias: the tendency to picture compound growth as if it were linear. People with stronger bias underestimate how fast savings grow and how much loans really cost. In their data, more-biased households borrow more and save less.
The straight-line guess adds €60 a year: €1,000 + 40 × €60 = €3,400. Compounding earns interest on the interest as well, and that gap widens every year.
Formula 1: future value
How much will an amount today be worth later?
FV = PV × (1 + r)ⁿ
- PV = the amount today
- r = the return per period (6% = 0.06)
- n = the number of periods
€1,000 × 1.06⁴⁰ ≈ €10,286.
Compounding frequency matters a little too. €10,000 at 6% for 30 years becomes about €57,400 compounded yearly and about €60,200 compounded monthly.
Formula 2: present value
Turn it around: what is a future amount worth today?
PV = FV ÷ (1 + r)ⁿ
This is the core of every "now or later" decision. Say someone offers you €10,000 today or €12,000 in three years:
| If your money can earn | €12,000 in 3 years is worth today | Better choice |
|---|---|---|
| 4% a year | ≈ €10,670 | Wait for €12,000 |
| 6% a year | ≈ €10,075 | Roughly equal |
| 8% a year | ≈ €9,526 | Take €10,000 now |
The answer depends entirely on what you could do with the money in the meantime. That rate is called the discount rate.
Try it now. Think of a choice you are facing: a cash discount for paying upfront, a bonus now vs later, a car lease vs buying. Write down both amounts and the dates, then discount the later one.
Formula 3: the rule of 72
A shortcut for doubling time:
years to double ≈ 72 ÷ annual return in %
| Return | Rule of 72 | Exact |
|---|---|---|
| 3% | 24 years | 23.4 years |
| 6% | 12 years | 11.9 years |
| 8% | 9 years | 9.0 years |
| 10% | 7.2 years | 7.3 years |
It works the other way too. At 3% inflation, prices double in about 24 years, so your cash buys half as much.
Real vs nominal returns
A return only matters after inflation. Economist Irving Fisher formalised the relationship:
(1 + real) = (1 + nominal) ÷ (1 + inflation)
A 6% nominal return with 3% inflation is a real return of about 2.9%, not 3%. Cash at 0% with 3% inflation is a real return of about −2.9% a year.
That is why our series insists money today is worth more than money in the future: today's euro can be invested, and tomorrow's has already lost some value to inflation.
Putting it to work
- Starting early beats saving more later. €1,000 a month at an assumed 6% grows to about €462,000 in 20 years but about €1.0M in 30. See your freedom number.
- Debt compounds too, against you. €3,000 on a card at 20%, paying €90 a month, takes 50 months to clear and costs about €1,400 in interest. See saving rate and consumer debt.
- Compare in today's money. Discount every future amount before comparing options.
Your checklist
- Calculate your own FV: current savings × (1 + r)ⁿ for 10, 20 and 30 years.
- Use the rule of 72 to find your doubling time at your expected return.
- Work out your real return: nominal return minus inflation, using Fisher's formula.
- Discount one "now vs later" choice you face this month.
Sources
- Stango, V. & Zinman, J. (2009). Exponential Growth Bias and Household Finance. Journal of Finance, 64(6), 2807–2849. Link
- Lusardi, A. & Mitchell, O. S. (2014). The Economic Importance of Financial Literacy: Theory and Evidence. Journal of Economic Literature, 52(1), 5–44. Link
- Fisher, I. (1930). The Theory of Interest. New York: Macmillan.
Educational content, not financial advice. Returns are illustrations, not forecasts. Investing carries the risk of loss.