Almost every financial blogger has written about compound interest. Still here I am bringing it up again because it’s such a powerful and critical concept in personal finance. I’ll do my best to make the math less dry and offer my own views on the power of compounding.
It’s never enough talking or writing to raise full awareness in people about compound interest. It’s so powerful and critical that I felt the need to write another in-depth series around compound interest. Today features the first post of this 3-post series where we revisit the concept of compound interest and see how its power can be leveraged.
Many of us may have doubted a well-told legend that Einstein once said
“Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it.”
I have my doubt too about who actually said that but compound interest is truly powerful, and no one should ever doubt it. It’s so powerful that it can make or break your finances.
What is compound interest?
Compound interest is interest on the principal plus interest on interest. This contrasts with simple interest, which is only the interest on the principal. What makes compound interest a beast is the interest on interest part.
Let’s look at a hypothetical example. Sara and Claire each had $100 and put it in a savings account that generated 5% interest annually.
Here’s a tweak that caused the difference: Sara was happy to receive the annual interest and decided to withdraw it to reward herself a matcha latte every year, knowing that next year she would recover the same interest. Claire also loves matcha latte but decided that her matcha latte could wait and left the interest intact in her savings account.
Time flies and 15 years has passed. Assuming there’s no inflation, interest rate has kept constant at 5% annually, and the price of a matcha latte is still the same, now Sara remains with the initial $100 in her savings account and has enjoyed 15 cups of matcha latte worth $75.
By holding off her craving for matcha latte, Claire managed to more than double her money. In her savings account, Claire now has the initial $100 plus a big fat $107.89 interest. That interest includes $75 interest from the initial $100 (just like what Sara got) plus $32.89 interest on interest accumulated for 15 years.
The effective interest Sara earned is equivalent to a simple interest because she used up her annual interest without letting it grow. From the disciplined case of Claire, we’ve seen the power of compound interest.
Compound interest for folks loving math
Alert: read this only if you really love math.
Here is the generalized formula of how a principal grows in t years with simple and compound interest, assuming a constant annual interest rate r compounded n times per year in the compound case.
Compound interest grows exponentially. And math never lies: the longer time you have, the significantly faster compound interest grows compared to simple interest.
Rule of 72
There is a rule of thumb to estimate how much time you need to double your initial money with compound interest: simply divide 72 with the annual percentage interest rate.
In the example above, with a 5% annual interest, Claire could expect to double her initial $100 in 72/5 = 14.4 years, which she actually did. If she was to put her $100 in an investment that returned 10% annually, Claire could have doubled it in only 72/10 = 7.2 years.
Note that this is only a quick estimate. Also note that the rule of 72 is less accurate when the interest or return rate is too small or too large.
The number 72 comes from an approximate of the natural logarithm of 2, ln(2). Interested in the math behind? You can find it here. People sometimes use the rule of 69.3 instead of 72 because ln(2) is approximately 0.693.
However, 72 is still a convenient choice because it can be wholly divided by a bunch of small divisors such as 1, 2, 3, 4, 6, 8, 9, 12, which cover the common range of annual savings interest or expected investment return.
Although I love matcha latte, coming up with the silly (and yummy) example for this post now makes me think twice everytime my craving for matcha latte strikes. Should I buy myself a matcha latte or hold off my impulse and patiently let compound interest do magic with my 5 bucks?
Why not both? Life is awesome with both matcha latte and compound interest!
I always try to see the big picture and plan for long term while still enjoying my lifestyle. As long as I automate all my savings and optimize them for compounding, I’m free to spend the rest of my expense allowance on as many matcha latte as I crave.
If you haven’t read this, head over to see how my simple 3-step budget can facilitate a long-term growth of your money while tolerating your impulse purchases.
Next up, we’ll discuss the cases when compound interest can make or break your finances. Stay tune!