What does starting late actually cost?

Unit closer — where compounding's arithmetic turns personal. The examples are illustrations of math, not instructions; the Academy trades in understanding, and this is the most expensive misunderstanding on the list.

The tale of ten years

One saver puts €1,000 to work at a steady illustrative 7% and waits 40 years: about €14,970. Another does exactly the same but starts ten years later — 30 years of growth: about €7,610.

Same amount invested. Same rate. Same discipline. The ten-year head start nearly doubled the outcome — because the head start happened at the WIDE end of the curve. Compounding's last decades do the heaviest lifting; a delay doesn't trim years off the flat beginning, it amputates them from the explosive end.

Why intuition gets this wrong

Human intuition is linear: "started 25% later, so I'll end up around 25% behind." The curve is exponential, and the gap it produces is closer to 50%. This mismatch between linear intuition and exponential reality is arguably the most consequential math error a person can make about money — and it cuts both ways: debt at compound interest runs the same explosive curve AGAINST the borrower. Credit-card rates run the rule of 72 in fast-forward.

The honest footnote

Real markets don't pay a smooth 7% — returns arrive lumpy, with drawdowns your Course 1 loss-lessons previewed and this course's Unit 3 will measure. So put a real path next to the arithmetic above. This is the broad US equity fund over as long a window as we hold:

Read it twice: once at arm's length for the trend, once close up for what the years in between actually did. The steady-rate examples isolate the TIME variable, not promise the path. What survives every complication: time in the curve is the one input nobody can buy back later.

Unit checkpoint ahead

TVM, compounding forward, discounting backward, and time's price tag — the machinery is installed. Unit 2 turns it on the question every investor asks first and measures worst: what did I actually earn?

Try it now

1. Recompute the tale with the rule of 72: at 7%, how many doublings fit in 40 years vs 30? There's the gap.
2. Say the debt version out loud: compounding works against borrowers with the same curve.
3. Now do it on the real path. Measure the chart below from its left edge to its right, switch it to Monthly if the daily noise gets in the way, and solve (end ÷ start)^(1/years) − 1 for the rate it actually delivered.

4. Feed that rate back into the tale in place of 7%. The ten-year gap does not go away — it is a property of compounding, not of the number you compound at.