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

Your Money or Your Life

By
Which is more important? Our money or our life? So why do we trade away so much of our life? Vicki Robin's classic book takes an in-depth look at how we can have a better relationship with money. Here are some of my highlights, though there's so much more great value in the book. I found it so inspirational after reading the foreword and the first chapter. While the backbone of the book is a 9-step plan, there are two concepts that really stand out - even if you never start the plan. One is the idea of "life energy" and our "real hourly wage". The other is the point of enough. Life Energy What is money? Vicki Robin comes to the conclusion that it is a form of life energy. It might sound a bit new-age, but it's like the old business saying "time is money". We exchange our time, and our physical and mental energy to get this thing called money. So when we use it we are effectively spending our life. The exchange rate Spending money is almost like...
Post a Comment
Read more

The real cost of owning a car

By
It's been about 10 years since I've owned a car. My wife doesn't own one either. "You must save a lot in petrol" That's one of the frequent reactions when someone discovers we don't own a car. "Of course, but it's just the tip of the iceberg" is the usual theme of my reply. Many people I've talked to just aren't fully aware of the real cost of owning a car. Or even that there are six different costs of owning a car. Six? Really? Yes. Occasionally a work colleague or friend will boast their car only costs $X per week. Of course it turns out only some factors have been counted. Sometimes it's just petrol alone. To some people, that feels like the only cost they pay each week. Why does this matter? You might be questioning the need for a second car in the household (or even having one at all). Or you might just be choosing which car to get next. Either way, to make an informed decision we need proper information. So let's look at...
2 comments
Read more

Where is the best place to live?

By
Where we live determines a lot about our life.  So today I'm going to share a resource that can help you decide where might be a good place to live.  It started with an article ranking Brisbane suburbs from 1 to 260 . That ranking was based on a set of 17 factors. Here are some of them. But all 17 may not be relevant for you. And some might matter more than others. So they developed a tool where you can rank the 5 factors most important to you and it will give you a personalised list of Brisbane suburbs that would be the best for you - based on those factors. There are also  Sydney and Melbourne  versions. On the results page, there's also a map that colour-codes each suburb by star rating, for each factor. For instance here's the map for public transport. Five-star suburbs are in blue. When you click on a suburb, you get the name and the star rating of that suburb - for whichever factor you select. I find this to be so enlightening. I choose not to own a car. Some...
Post a Comment
Read more