The Beauty of Compound Growth

Just a head’s up, this article will include quite a bit of math. I’ll do my best to explain it in simplistic math as well as I can, but when it comes to numbers, you’re just going to have to trust me.

Compound growth is the reason that people earning an average salary can become millionaires. It’s a wonderful tool in finance that can literally change your life.

It better be good now that I said that, right? Well, here’s what it is. You tell me.

SIMPLE EXPLANATION OF COMPOUND GROWTH

Compound growth is the mathematic principle that something (i.e. money) will grow faster and faster over time. So, simply, imagine your money grows from \$1,000 now to \$2,000 in 10 years, \$4,000 in 20 years, \$8,000 in 30 years, and \$16,000 in 40 years. Your money just doubled every 10 years without you putting any more in.

This 8th wonder of the world happens because the more money you have, the faster it grows. So 8% of \$1,000 is \$80. Reinvesting that money into the same account means you now have \$1,080. For simplicity, let’s say after 10 years, you now have \$2,000 (it should actually be more). Basic math tells us 8% of \$2,000 is \$160. You earned twice as much as you did the first year.

Moving further another 10 years, your money will have doubled again to over \$4,000. I bet you can guess what 8% of \$4,000 is. It’s \$320. Now, that first \$1,000 you put in will earn your \$320 in one year. How about another 10 years? Let’s make it \$8,000 now. An 8% growth on \$8,000 is \$640.

Last time, 10 more years into the future and your account has grown to \$16,000. Taking 8% of that leaves us with \$1,280. That’s much more than your initial investment. Even more wonderful is that I simplified the math so that we were only doubling. Your balance should actually be much more than this if you earned 8%.

Do you see where I’m going with this? The more money you have, the more money you earn. We expect it to grow as a percentage of your investment. We can simply say if the percentage stays the same, but your account grows, the actual dollar amount it grows will continue to get larger and larger.

MATHEMATICAL EXPLANATION

Although I did a bit of math in the previous section, it wasn’t extremely thorough, nor was it 100% accurate. Those numbers were all rounded down in order to prove a point. If you’re looking for actual numbers, this is where you’ll find it.

First, I’d like to show you how you can calculate your growth in dollars. This equation is pretty easy:

Initial Investment x Percent Growth (as a decimal) = Growth (\$)

Going back to our \$1,000 investment with an 8% return, we can use:

\$1,000 x (0.08) = \$80

Additionally, we can find what our new total balance would be after our growth by tweaking the equation a bit:

Initial Investment x (1 + Percent Growth) = Total Balance (\$)

For our example, this is:

\$1,000 x (1 + 0.08) = \$1,080

Pretty basic stuff, I think. This will be the foundation for our other calculations, and will give a starting point to build our next equations.

Next we can look at an equation that will show how much our balance will be after several years. Using this equation will allow you to see the amount you can expect to have in your account after however many years you choose, at whatever growth rate you choose, and with any initial investment amount you choose. Here is the equation:

Initial Investment x (1 + Percent Growth) ^ # of Years = Total Balance (\$)

A bit more confusing, I know. Basically you are taking your growth rate and using your years as an exponent to find how much the total growth will be. To break this down, let’s say you expect 8% growth every year, and you want to find by what % your money will have grown. For 3 years of growth, we can find that your money will grow to become:

(1 + 0.08) ^ 3 = 1.08 x 1.08 x 1.08 = 1.26 or 126%

Essentially your money will be 126% of what it was when you started. So when we multiply that by our initial investment, we find:

\$1,000 x (1 + 0.08) ^ 3 = \$1,260

After 3 years, our money will now be \$1,260. This will represent an increase of \$260, or 26% growth. Not bad. What’s even better is that it grows even more the longer you let it ride.

Here’s what your account would be at if you invested \$2,000 and let it grow for 20 years and received a growth rate of 7%:

\$2,000 x (1 + 0.07) ^ 20 = \$7,739

What about a \$3,000 investment for 40 years and a growth rate of 9% per year?

\$3,000 x (1 + 0.09) ^ 40 = \$94,228

Seriously, whatever numbers you want to plug in, you can. Make sure you’re realistic though. The general consensus on long-term growth rates is to expect about 8% per year. You also probably won’t be investing \$25,000 per year if your salary is \$30,000. The best way to plan is to plug in your real numbers.

Next, I’m going to set up a pretty realistic scenario. You’re going to save \$3,000 at the beginning each year for the next 20 years, and you’d like to know what your investments will grow into by the end of year 20. Based on market history and generally accepted information, you’re expecting a growth rate of 8% per year throughout the period.

The following table will show each year’s investment, the formula used to find your ending balance, and the actual ending balance you can expect. At the bottom, we will sum what all of your returns have grown to and see how well your money did over that 20 year period. I’m going to preempt this table by pointing out the fact that your total investment will be \$60,000 over this 20 year period.

Here we go:

By the end of 20 years, your \$60,000 invested will grow to nearly \$150,000. As you can see in the chart, the money that had more time to grow was able to become substantially larger than the investments made later on. This is why you always hear “start while you’re young.”

WHY COMPOUND GROWTH MATTERS

Most people don’t really use this type of math on a daily basis, obviously. It is important to understand it, though.

A lot of younger people now have the ambition to begin retiring early and achieving the freedom to do whatever they please, but unless they’re making massive amounts of money, it will be pretty unachievable without a solid understanding of their own personal finances and the tools necessary to reach their goals.

If you don’t want to, or plan to, work a 40+ year career, this is critical information to understand. Find out how to effectively grow your money so that you will have the ability to live comfortably even after you’re done working. Just putting a good chunk of money into a savings account isn’t enough. Your “high yield” savings account is somewhat misnamed as well. Even the top paying accounts are just above 1%. After inflation, your high yield savings account basically yielded nothing.

Similar, and even worse, is simply having all of your money in a regular savings account or cash. Every year, inflation makes currency worth less than it was in the past. Inflation is the reason older people talk about buying burgers for 5 cents or a brand new car for \$1,000.

If you’re working for your money, but you don’t have your money working for you, inflation will eat up any plans you have for retirement. Remember the \$60,000 we invested in our example? If you don’t invest it, you’ll still have \$60,000, but your money won’t be worth as much as it is right now.

Learn to invest and use compound growth, otherwise your early (or normal) retirement plans will be based on the lottery or an inheritance. Not the greatest plan.

What is your investment plan to reach your goals? Feel free to share any strategies or information you come up with in the comments. Let’s help each other!