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

Ethical Investing for Australians

By
I write about investing, because it's a key part of life. Spending less and investing means an automatic income. An automatic income means we can work less (if we choose) and definitely stress less. But where to invest? What to invest in? Many people expect their money to be invested responsibly and ethically - rather than making money through things like cigarettes, weapons, casinos, adult entertainment, environmental destruction, and pollution from fossil fuels. Those are all things we could probably do with less of. So how do we invest to get good returns - and to have a positive effect on the world? Here are some sources I've seen: Ethical Investing in Australia At Frugality and Freedom , Michelle has done a fair bit of research into Ethical Investing in Australia . For herself, she's chosen Bank Australia for banking, Australian Ethical for superannuation, and two exchange-traded funds ( FAIR and ETHI ) for her share investing outside of super. She also gives detail...
1 comment
Read more

How to waste a year's wages

By
A friend recently asked me why it is that so many people (on good incomes) are struggling to save. Often the big three money areas are housing, transport and food. In one sense these are necessary items. But what we spend on them is often way more than necessary. I crunched some numbers on how much extra my wife and I could spend on these things - if for some reason we wanted to burn our money. 1. Housing Our apartment is fairly nice, but also cost-effective. I've mentioned how choosing it saves us $1,800 per year , compared to a similar one we saw. The high end of 2-bedroom apartments in our suburb is $305 per week more than our apartment. Not $305 per week. $305 per week more than ours is. I cannot get over that. Sure it's new and modern-looking, but that's a lot of money. It's an extra $15,860 per year above what we pay. 2. Transport The Australian Automobile Association lists the costs of owning and running a car. It includes many often-overlooked c...
4 comments
Read more

Don't dump on charities

By
Netflix causes mass dumping. Here's an alternative. January is usually a big month for physical donations to charity. In 2019 it's been over-the-top (literally) as charity donation bins have been overflowing with items. The Netflix series "Tidying Up" by famous declutterer Marie Kondo (see her book ) has inspired many to declutter their homes. But in the process they've cluttered the streets. What's so bad about donating? When the bins overflow the extra items are thrown away. Having been in the weather, the rain and on the ground, they are classified as contaminated and cannot be sold. To make it worse, much of what fills the bins is not good enough to sell, and is also dumped. Bad donations hurt charities 13 million dollars. That's how much it costs charities to deal with all the junk we dump on them - 60,000 tonnes a year. Lifeline says half its stores have stopped accepting donations. We might think we're helping, but that's a lot ...
4 comments
Read more