How fast can your money double?

Here’s a riddle that checks how well you understand the mathematics of growth. Let’s say we have a pond with a single lily pad. It’s a special lily pad that grows very fast, doubling in size every day. It’s expected that on the 30th day, the pond will be fully covered by this lily pad.

- KEITH LIM

Here’s the question: Given what we know about the pond and the lily pad, on which day was half of the pond’s space taken up by the lily pad? Try coming up with your own answer first before reading on!

It’s tempting to answer day 15. After all, if we’re solving for when the pond is halfway filled, then the halfway point of our 30-day time horizon feels intuitive. But the correct answer is actually day 29! If our lily pad doubles in size every day, that means if our voracious lily pad covers half the pond on day 29, it will cover the whole pond on day 30, since a doubled half makes a whole!

This riddle illustrates the importance of understanding compounding growth. Compounding is when an object’s growth relies on its size in the previous time period. Investing works this way: a 10-percent growth applied to P10 is just P1, but apply that 10-percent growth to a billion pesos, and your wealth grows by P100 million. When it comes to investing, the amount of capital you start with matters.