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Money Can Grow: The Power of Compound Interest

Updated: Sep 9, 2023

The compound interest formula looks complex and intimidating.

The compound interest formula. A = P(1+r/n)^nt

But this mathematical formula holds to key to your financial freedom.

Fortunately, you don't need to understand the math in order to use compound interest to your advantage. There's always the trusty moneychimp compound interest calculator available to do that for you. However, understanding what compound interest is, and how it works in practice will help you make informed choices for your financial future.

In the simplest of terms, compound interest is when you earn interest on your principal plus your interest instead of just on your principal.

Simple Example:

Using nice round numbers that are easy to understand.

Without compounding, earning 10% annual interest on a $100 investment would mean you earn $10 every year. Each year your balance would grow linearly, by $10 a year. Starting off with a small sum it would take you 99,900 years to grow that original $100 to a million dollars.

a graph showing how $100 grows to $300 over 20 years without compound interest

With compounding, the 10% you earn each year grows as your investment grows. The first year you earn $10 on your $100 principal and then reinvest that $10 you earned. The following year you earn 10% of the $110 you have invested, so you earn $11 instead of $10. This pattern continues so that after 10 years you're earning 10% of $259.37, so you earn $25.94 in interest instead of $10.

a graph showing how $100 grows to $672.75 over 20 years when compounding interest

After 10 years, the difference is obvious, without compounding your original principal has grown only to $200 because you're only earning interest on the original investment. With compounding you get to $259.37 because you're earning interest on the original principal plus the accrued interest.

The difference grows over time:

After 20 years, you would have $672.75 with compound interest compared to $300 with simple interest. Compounding allows your money to grow more than six times the original investment in just 20 years.

In fact, it only takes 97 years for $100 to grow to $1,035,357.80 all on its own with compound interest. 97 years is a lot more reasonable than 99,900 years. But it's still too long to be useful for a mere human lifespan of 80ish years.

Keep Investing:

The good news is that you're (most likely) still earning money, so you can keep investing more each year (or more often). When you add in additional investment, then compound growth starts to change your life.

Let's say you decide to invest $100 every month. Making the same assumptions as above (10% annual interest) it would only take 46 years to get to $1,053,187.78. What if you invested $200 a month? 39 years to break a million. $500 a month? 30 years. That's starting from 0. That's the power of compounding.

Real Life:

Unfortunately we're not guaranteed to earn 10% interest on our investments every year (although 10% is the historical average of the stock market). To be safe we should consider that there's inflation, and that while the stock market does always go up over time, it doesn't do so every year. More realistic (inflation adjusted) estimates of average rate of return for retirement planning are between 5-7% depending on your asset allocation.

So in real life you need to invest about $1000 a month (in a low cost whole index tracking fund!) for about 30 years in order to get to a million dollars. (This works in any currency by the way, 1000 dirhams a month for 30 years = a million dirhams).

Your Life:

Maybe a million dollars is too much, or maybe it's not enough for you. How do you know how much money you need for your future (your FI number)? You can calculate it using the 4% rule (multiply your annual expenses times 25). But first you need to be tracking your expenses so you have authentic numbers to base your calculations on.

How long will it take you to get to your FI number? You need to know your annual income and expenses to calculate your savings rate. Then you can use the handy chart in my What's Possible post to see how long it will take you to get there.

Take away:

If you want to be financially independent in 10 years, and you're starting from zero, you will need to invest between 65 and 70% of your income. That's a big ask, but it's possible. That's the savings rate my family has maintained for the past several years.

However, you don't have to go so extreme, you can easily plan a longer path and keep your savings rate at 30% and still retire earlier than most of your peers. Maybe faster if you already have some assets.

The key with compound interest is TIME. The best time to get started investing is today, the second best time is tomorrow. Need help getting started?

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