Archimedes Finance

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The magic of compounding returns

Lesson in Course: Investing basics (beginner, 4min )

It's a mistake to underestimate the cost of time. Are we missing out on compounding growth?

Compound interest is the eighth wonder of the world. He who understands it, earns it … he who doesn’t … pays it. 

-Albert Einstein 

What is compound growth or interest?

Compound growth, or compounding, happens when an investment creates earnings, and then those earnings generate earnings. A simple example is the interest we earn in a bank account. Imagine we deposit $100, and we make $5 worth of interest the first year. The following year, we will earn interest on both the $100 deposit and the $5 we made the previous year. The effects of compounding become stronger the more time we give an investment to grow.

Speed of compounding

To get an idea of how fast our returns compound and the difference it makes in the long run, let’s look at an example of our two friends, Casey and Alex. They are both 24 years old, employed, and have a 401(k) at work.


Casey is our responsible friend, and she starts participating in her 401(k) this year. She sets aside $1000 a year towards retirement, contributing for the next 10 years, and then stops after that.


Alex, while responsible, prefers to live in the moment. He puts off retirement saving for 5 years and spends the money on traveling. After 5 years, he follows Casey’s footsteps and contributes $1000 a year until retirement.

Let's see how much money they have after 10 years:

Casey's first 10 years

Casey has $16,888 after 10 years. At 34, Casey's earnings per year is now more than her yearly contributions of $1000. Her investments add more to her account than she does!

Alex's first 10 years

Alex only has $7,564 after 10 years. At 34, Alex is lagging behind Casey quite a bit due to his late start to compounding.


How about when Alex and Casey are 50?

Casey's progress at age 50

We might assume at this point, Casey is far behind Alex since she stoped contributing at 34. At age 50, Casey has $49,857 and is only behind Alex by less than $3000. By starting 5 years before Alex, Casey gives her original investments more time to compound, which helped her account grow faster longer

Alex's progress at age 50

Contributing $1000 every year, Alex only barely manages to catch up to Casey at age 48. At age 50, he has $52,436 saved for retirement. Remember, Casey stopped contributing 14 years ago!

At age 50, Alex contributed $22,000 to his retirement account while Casey only has contributed $11,000. Yet, due to Casey starting 5 years before Alex, they have almost the same amount of money even though Alex put in double that of Casey.


The benefit of compounding early

Now let's check out the effects of compounding at retirement.

Casey at retirement

Casey has not contributed a penny more to the $11,000 early in her career. Over time, her investment's compounding growth netted her $126,558, or an 1150% increase.

Alex at retirement

By age 65, Alex has contributed a total of $37,000 over the years. Compounding growth on his investments have earned him $134,561, a 363% gain. His account ends up with $34,000 more than Casey's.

The astounding difference when comparing Casey's gain of 1150% compared to Alex's gain of 363% points back again to Casey starting 5 years earlier. It’s important to note the effects of compounding are magnified by higher rates of return. E.g., at 1% growth, the difference would be much less noticeable. As of 2019, the S&P500, since inception, has historically returned 10% year over year. After adjusting for inflation, 7% has been a reasonable real return for estimating.

Here's a video that shows compounding in another light.


By starting earlier like Casey, the effect of compounding allows us to earn more despite contributing significantly less than we think. Starting to invest early, no matter how small, and being consistent over time will lead to significant gains in the long run. Be patient; compounding will take care of the rest.


What is Compounding?

When an investment creates earnings, and then those earnings generate earnings.

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