By Math Is Fun, January 7, 2022

Son is turning 7. It’s time for an investment class. OK, not really. But it doesn’t hurt to try, right?

So I gave him a 100 dollar bill. “Let’s say if you put this bill in a bank, the next year you will have 110 dollars in your bank account.”

(Well, this is very hypothetical, and there are very few banks in the world right now that will give you 10% interest, as of January 2022. In fact, I think some banks right now are having negative interest rates, so next year you might have 99 dollars in your bank. But 10% interest isn’t unheard of going back some years.)

“Why would a bank do that?”

“Because they can lend the money to a company and get 120 dollars back in a year. So the bank will actually make money by taking your money. For you, you will earn 10 dollars for every 100 dollars you put in your bank for the year. That’s called interest.” I explained first, then asked a question, “So how much money will you have after 10 years?”

“200? Since I earn 10 dollars a year, I will have 100 dollars interest after 10 years.”

“The answer is 259 dollars and 37 cents. Quite a bit more than you think.”

“How come?”

“Let me explain. You have 100 dollars to start. After 1 year, the bank gives you 10 dollars as interest. How much interest are you getting after 2 years?”

“20 dollars?”

“A little more than that. See, after the first year, after you got your 10 dollars interest, you now have $110. The second year the bank will give you the interest based on $110, not $100. So your interest in the second year is $11. And your total balance is $121, not $120. Similarly the interest for the third year is $12.1, not $10, etc. etc.” I explained.

I continued to summarize: “This is called compound interest. It means interest is calculated on top of the initial balance plus past interests. Your money grows faster and faster when time goes by. This is the secret sauce of investing.”

For the annual interest rate of 10%, here is how much you will have with the initial balance of $100.

Now | $100 |

After 1 year | $110 |

After 2 years | $121 |

After 3 years | $133.10 |

After 10 years | $259.37 |

After 20 years | $672.75 |

After 50 years | $11739.09 |

After 100 years | $1,378,061.23 |

Right, after 100 years, $100 with 10% interest rate will go to 1.38 million dollars! This is the power of compound interest. This is the power of investing.