A few weeks ago, I wrote about how a small regular investment grows over time with compounding interest. A reader recently sent me an illustrative story about compounding that I want to share.
Once upon a time, there was a king who collected almost the entire rice crop harvested by his subjects as tax, promising to give it back during tough times. After many good years, there came a year when there was no crop. However, the King was stingy and unwilling to return the rice as promised. A clever girl did a favor to the king, and then asked for a reward.
The reward that she asked for was that she would receive one grain of rice on the first day, and double that on the second day. On the third day she would receive twice that from the second day. And so on for 30 days. The king thought that it was a modest request and granted it to the little girl.
However, when the King started to pay the reward, he realized what it would become.
On day 6, the little girl received 32 grains of rice.
On day 12, the little girl received 2,048 grains of rice.
On day 18, the little girl received 131,072 grains of rice.
On day 24, the little girl received 8,388,608 grains of rice.
On day 30, the little girl received 536,870,912 grains of rice.
After 30 days, she received a total of 1,073,741,823 grains of rice. (After I read this, I did the math in Excel to make certain that it is correct.)
As you can see, the increase from day to day gets larger the more days that the girl has been “investing.” While no investment offers 100% daily returns, the same concept applies to lower returns and longer periods of time.
I am certain that there are similar stories in many cultures. What version of this story have you heard?
Brian Hock, CMA, CIA