Plot principal × (1+r)ᵗ — the curve bends sharply upward as time grows. Compounding rewards patience.
Slide principal, rate and years
compound → $14,974 (+$13,974 interest)
compound: A = P(1 + r)ᵗ · simple: A = P(1 + r·t)
Why the curve bends upward
Linear growth (simple interest) is a straight line. Compound growth follows P × (1+r)ᵗ — an exponential curve. Early on the two look similar; over decades the exponential one rockets away.
Try it
$1,000 at 7% — value after 10, 20 and 40 years?
≈ $1,967, then ≈ $3,870, then ≈ $14,974. The last 20 years add far more than the first 20.
The steep part of the curve is at the *end* — which is exactly why starting early matters so much. Time, not timing, does the heavy lifting.