Ah, compounding. Perhaps the most well known quote about compounding is an apocryphal one attributed to Albert Einstein.

“Compound interest is the eighth wonder of the world.”-[Almost certainly not] Albert Einstein

Regardless of the provenance of the quote, the gist is mostly correct. Compound interest is so powerful that it is very difficult to properly do compounding math in one’s head. The ‘rule of 72’ helps us with approximations. The rule says that if you divide 72 by the rate of return, the result is the amount of years it takes something to double. So for instance, if something returns 10% per year, we expect it to take 72/10 = 7.2 years to double. The actual answer is 7.28 in case you’re curious.

This is quite a bit shorter than the simple 10 you might get from saying that 100% return is doubling, and there are 10 10%s in 100% and therefore it will take 10 years.

Assuming 10% annual returns (which I’ll note is quite high), that means if you invest a dollar for 7.5 years you expect it to double, for 15 you expect it to quadruple, for 22.5 it will be 8x what you invested, and 30, 16x.

30 years is still shorter than many working careers and retirements, if you start working at 25, you might have savings invested for 35 years until you’re 60, and again for another 35 if you live till you are 95.

This is why compound math is so important.

It is also very important to understand when compound math is being used to trick you. I have seen many life insurance policies pitched to people around 30 years old that guarantees to be worth seven times what they put in by the time they are 80. This can sound great. However, if you crunch the numbers, you’ll find that an investment that increases seven-fold over 50 years has given you a return of under 4% per year. Not so attractive, perhaps.

Compound returns are why it can be so valuable to start investing early. A couple with $500,000 invested at age 40 and earning 7% per year will see that number grow to $2.7 million at age 65 with no further savings. If it takes you ten more years, only reaching that $500,000 by age 50, at age 65 you’ll have about $1.4 million.

In fact, to catch up to the same $2.7 million as the couple that reached $500,000 by 40 and didn’t save any more, the couple with $500,000 at 50 would need to save $53K per year from age 50 until 65.