The Hockey Stick Effect
Human brains are wired for linear thinking. If you take 30 steps linearly, you end up 30 meters away. If you take 30 steps exponentially (doubling each time), you end up circling the Earth 26 times.
In the simulation above, notice how the "Total Value" line (blue) barely separates from the "Money Invested" line (gray) for the first 5-10 years. This is the "Valley of Disappointment." It feels like nothing is happening.
But keep dragging the time slider to the right. Suddenly, the curve bends upward. The gap widens. In the last few years of a 30-year horizon, your portfolio might grow by more than your entire salary—purely from interest on interest.
Time is the Exponent
The formula for compound interest is \( A = P(1 + r)^t \).
Notice that time (\(t\)) is the exponent. It does the heavy lifting. Doubling your savings rate (linear) is good. But doubling your time horizon (exponential) is transformative.