The Magic of Compound Interest
Have you heard about the magic of compound interest? Do you cringe at the thought of old high school algebra word problems on exponential growth? If so, this note may be for you.
Albert Einstein purportedly said that compound interest was “the most powerful force in the universe” and “he who understands it, earns it; he who doesn’t, pays it.” I’m not sure he actually said any of those words but they capture the spirit well.
Compound growth simply means that a value is growing by a constant factor each period. The growth rate is added to one and the value from the previous period is multiplied by that factor to get the next period’s value.
A simple example may help:
- Assume there are 100 hungry great white sharks swimming off the coast of Cape Cod and their population is growing 10% per year.
- The growth rate is 10% and the growth factor is 1.1 (or 110%). At that rate, there will be 110 sharks in one year and 121 in two years (not 120). To get next year’s number, you multiply the current year by 1.1.
- In year 3, there will be 133; in year 4, there will be 146; and by year 5, there are 161 sharks. That’s the “magic” in compound interest — the percentage growth rate is constant but the number of new sharks grows faster each year.
Here’s a good trick for your next cocktail party. If you know the growth rate and want to know how many years it takes for something to double, you can try to remember your high school exponential functions or you can simply use the rule of 72:
- Divide the growth rate (e.g., 10%) into 72; the answer is a very close estimate for the number of years it will take for something to double at that rate of growth.
- If you’re wondering, at 10% growth, the shark population will double in ~7.3 years (the rule of 72 predicts 7.2 years).
- Alternatively, if you have an IRA that is averaging 6% annual returns and you’re neither contributing to it nor taking distributions, its value will double in ~12 years.
Lastly a note on semantics.
- Compound growth and exponential growth are synonymous terms.
- The term growing exponentially is often used to imply something growing quickly. Not necessarily true. For example, if your savings account offers 0.2% interest, that’s exponential growth but it’s certainly not fast growth.
As usual, Einstein was right — it’s better to earn compound interest than to pay it.
Don’t swim near the seals.