A Few Examples That Show How Counterintuitive Compounding Is
Compound interest is the eighth wonder of the world. He who understands it, earns it. He who doesn't, pays it.
- Einstein1
Example: Bank account
Investing money in a bank account for 10 years produces more than double the interest as investing it for 5 years, because in the former case, the interest at the end of 5 years gets reinvested for the next 5 and earns more interest.
Interest is linear wrt the amount invested but more than linear wrt the time invested.
Example: Bank account
Investing 1 lakh in a bank account for 10 years produces more interest2 than investing 2 lakh for 5 years3.
Example: Mutual fund loss
If your portfolio loses 10% this year but grows by 10% the next, you’re back where you started, right? Wrong! Imagine you started out with ₹100. The 10% loss puts you at ₹90. Then the ensuing 10% gain adds 10% x ₹90, which is ₹9, leaving you with ₹99, which is worse than the ₹100 you started out with. Equity losses have to be balanced out with bigger gains: a 10% loss needs to be offset by a 11% gain. A 20% loss needs to be offset by a 25% gain4.
Example: Retirement
A person invests for four decades, and then retires. After three decades, he has a portfolio of 1.8 crore. How much will the portfolio be worth after four decades? 2.4 crore? 3? Actually, it will have exploded to 4.5 crore5! 60% of the portfolio growth has occurred in the fourth decade! Not 25% as you’d expect if it were linear.
Example: Saving early for retirement
Consider two people, Amy and Sam. They’re both 22. Amy invests $200 a month for 6 years and then stops. Sam doesn’t invest for 6 years, and then starts saving the same $200 a month till he’s 65. They both earn 12% per year. Does Sam end up with more money at 65? Amy invested $14K in total, and Sam, $89K. So you’d expect Sam to be much richer, right? No, both have $1.6 million at age 65. The reason is that Amy stayed invested 6 years longer.
Example: Credit cards
When I maxed out my credit cards, and then started repaying them, though I repaid the entire amount due over 2-3 months, and thought that I’d mostly repaid it, I still had to make a substantial payment. Then there was another payment to make. That’s why Einstein said that those who don’t understand compound interest pay it. It’s a powerful force, and you want to be on the right side of it, by being an investor rather than a borrower.
Example: Covid
Remember how quickly Covid exploded? First, it was something in Wuhan. Second, it was global, but in the news — most of us didn’t know anyone who experienced it. third, we all heard of family, friends and neighbors who died. It exploded so quicly because it’s exponential: more the infected, the more people they infected.
A shortcut
When the interest rate and the number of compounding periods are both low, you can approximate compound interest as simple interest. For example, a three-year investment that yields 3% per year can be approximated to 9%. You can’t use this simplification to the retirement corpus after a whole career.
I don’t know if Einstein really said this, but it makes sense regardless of who said it.
Not the amount in the bank account by the end of the investment period.
Why? If x is the interest earned from investing 1 lakh for 5 years, investing 2 lakh for 5 years produces 2x. Investing 1 lakh for 10 years can be modeled as two investments for 5 years each, each producing an interest of x, amounting to 2x, plus the effect of compounding where the interest from the first 5-year period earns more interest in the second 5-year period. 2x + compounded interest > 2x.
Which is why, for a mutual fund, avoiding losses is more important than achieving gains.
Assuming 10% return and 1 lakh investment per year.