Skip to main content

The magic of compound growth

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.

Comments

Popular posts from this blog

Simple phone

I get my fair share of teasing for still using a Nokia phone. So I feel quite vindicated that someone has now invented a new non-smartphone . It's pitched for those who want a decluttered life. Instead of features, its selling points are things like "reclaim a little quietude from the constant intrusions of technology", "no internet connection, no app store and definitely no camera for taking selfies". One quote from the article said "as smartphones get bigger and bulkier, there is a place for something small and simplified, without all the functions." That kind of statement resonates with me. Not just for phones, but for so many areas of life - including the houses we live in.

Why own a car, when you can go get?

That's the slogan of one company providing an alternative to car ownership. Here's our experience with them. Why not just have our own car? Another time I'll write a full post about that, but suffice to say that car ownership is a pain in the neck. The servicing, the maintenance, the repairs, the parking, the traffic, the registration, the insurance, the cleaning... For my wife and I, about 98% of our transport needs can be done on foot, by bike, by train, bus or ferry. Maybe 99% if you include rideshare. So we choose to avoid the pain (and cost) of car ownership. However, car use (I think of it separately from car ownership) can be handy in certain situations. We had one of those situations last weekend. Here's how it went. Booking a car My wife signed up for GoGet , and booked the car online for the time window she needed it. As a first-timer, she received her little membership card in the mail. On the day of the booking, GoGet sent her a reminder email about 20 minut...

The Latte Factor

For the first time ever I'm reviewing a novel. Latte Factor is a short story  - around 120 pages - and is equal parts of inspirational story and financial education. The combination of the two is quite rare, and done quite nicely. The story is about Zoey Daniels, associate editor for a travel magazine. Although she's never been outside the USA  - "a travel editor who's never travelled". She struggles with money and is considering a higher-paying job at the company her friend Jessica works for. The job would provide more income, but would also be more stressful and demanding. She already has a nightmare about being on an increasingly-fast treadmill that she struggles to stay on. Her current boss Barbara - aware only of the money situation - suggests she talk to Henry at the coffee shop. This peculiar suggestion is where Zoey's life begins to turn a corner. Spoiler Alert Being a book of fiction, I don't want to spoil the story for you. It's a book you ca...