Skip to main content

The magic of compound growth

Image
By

Compound Interest. Described by Albert Einstein as the 8th wonder of the world. Many people don't fully grasp its power and miss out on the magic.

Here's a quick example

For 30 days, would you rather (A) get $100 per day, or (B) get 1 cent doubled every day (ie. 2 cents on day two, 4 cents on day three, 8 cents on day four).

Quickly. What's your immediate answer?

On intuition, lots of people go for Option A. Why? Because $100 sounds so much more than 1 cent.

How do they compare?

Do the maths, and Option B wins by miles.

By Day 15, the 1 cent per day has grown to $163.84 per day.

Over the first 18 days, Option B accumulates $2621.43 (compared to $1800 for Option A). It just snowballs from there.

By the final days, Option B is getting millions per day and ends up with a total of $10.7 million. Meanwhile the total for Option A is just $3,000 ($100 x 30 days).

(Sidenote: Even if Option A was $100,000 per day, option B would still win.)

Life in slow motion

Investing can be much the same - just slower. Let's say for example that my retirement account averages 9% over the long term and I'm thinking of adding $10,000 to it this year.

At first I might think that $900 (9% of 10,000) isn't a huge amount. $900 per year for the next 30 years would be $27,000 extra in later life. That sounds reasonable, but is a big underestimate.

Because the $900 goes back into the investment, it also grows at 9% and so it snowballs.

Do the maths for a 30-year timespan, the $10,000 actually turns into a much bigger number...

$ 132,676.78 (to be precise)

Woah! That's not a 27k profit. That's a 122k profit.

If we only knew

Realising this maths can help us make better decisions.

If we think that investing $10,000 earns us just $900 per year (the dotted line below) we might be tempted to spend the ten thousand instead.

Once we realise that we can turn $10,000 into a six-figure sum (the solid curved line below) we might be more keen to invest.

So how does the maths work?

I get that a lot of people have maths-phobia from school. So let's break it down.

To work out what our money becomes in one year we multiply by one plus the rate of growth. For example, 9% growth would mean multiplying by 1.09.

eg. $10,000 x 1.09 = $10,900

For multiple years we keep multiplying by that rate.

eg. For two years, $10,000 x 1.09 x 1.09 = $11,881

Or if you're comfortable with exponential mathematics, put the rate to the power (or exponent) of the number of years.

eg. For 30 years, (1.09)30  x $10,000 = $132,676.78

(Remember to do the exponent part before multiplying by the amount - otherwise you'll get crazy numbers)

Notes

I haven't taken tax into account, because I was actually looking at the effect on my retirement savings and the 9% growth rate is after tax has already been subtracted.

Related Reading

$200k for a coffee and a sandwich

Get my monthly email for future money-maths items like this.

Disclaimer

This information is general in nature and does not take into account your personal situation. It is not financial advice. If you need specific advice on your circumstances or finances you should speak to an expert.

Read more about:

Comments

Post a Comment

Popular posts from this blog

My mug shot

By
This is every mug I own. How many did I buy? Zero. They seem to just appear. I don't even drink tea or coffee. In winter I have might have a hot chocolate or cocoa. So 9 mugs seems like a lot. How does this happen? I reckon most mugs are gifts. There are two reasons for this. 1. It's a safe bet. People need to drink. It's kind of like buying your dad socks for father's day. But the difference is that socks wear out and need replacing. Cups don't. One of these mugs i received as a kid in the 90s. It still works fine. Now it has 8 friends. 2. It's often for what's on the mug. It might be a greeting card-style message, or a sports team logo, or something humorous. It's a good thing that something functional can also provide an inspiring message or pleasant memory as you use it. But the problem comes when we have too much. If I use the cup my sister gave me at Christmas, then I'm not using the 'awesome brother' one she already gave m...
2 comments
Read more

Less Clutter More Cash - now available

By
Do you feel like you have too much stuff? Is your home full of things you never use? Would you like to swap them for cash? We did My wife and I have sold more than 550 items online as we downsize and we've learnt a bit along the way. I've put some of our best tips into this handy ebook. I hope you can use these tips so you too can have less clutter and more cash. Enter your email address below to receive the book for free. Less Clutter More Cash Get my new ebook for free. PS. This will subscribe to the But Wait There's Less email list, so you'll know when the new updated version of the book is available. You can unsubscribe at any time.
Post a Comment
Read more

Four Thousand Weeks - Time and How to Use It

By
First question. Why 4000 weeks? That's the average human lifespan. If you're reading this you've probably used up 1000 already. If you're a bit older you may have only 2000 left. Maybe just 1000. That can be a startling thought - given how quickly each week goes by. There's so much wisdom in this book, it's hard to summarise it briefly. But I'll give it a go.... Face the Finitude If time was infinite, we could work for 40 years and not miss out on anything. We could spend frivolously as we could always earn more money later. But in the real world there are time limits. Even if we have enough money to escape the nine-to-five, our time (though more plentiful) is finite. Just like money, we will run out if we fritter it away on low-value options. "Face the Finitude" has become one of my internal phrases now. It's my reminder that I don't have infinite time to waste. It may be helpful to think of it like money. eg. I might like something, but d...
Post a Comment
Read more