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

My October challenge

Decluttering can be overwhelming. I've been stuck. Shelves and boxes and drawers full of stuff I should go through but not sure where to start. Aaagh - there's so much of it. The solution? So for myself (and for you if you want) I've developed a strategy. I've picked 31 categories in advance. I plan to tackle one item per day of October. If I miss a few that's OK. The point is to overcome overwhelm. To focus on one thing at a time. To move forward instead of being stuck. My favourite way to declutter is to sell online . (I even wrote a  free ebook of tips for selling online). I also like to recycle or upcycle things. Wanna join in? I've chosen categories where I think most people would have excess. If there's a category you have already dealt with, that's cool. Have a rest day - or go even further in one of the previous areas. The list Ok so here's my plan for this October. Bookmark this post or download the picture of my notes. For each category I ...

5 Reasons why we hoard - and they're wrong

"Less is More" is one of the catch-cries of downsizing. Often the fewer things we have the more we value them. So it's a great title for a book that's basically a manual for how to de-clutter your home. The introductory chapter of Less is More: How to De-clutter Your Life gives some great insights into why we find it so hard to reduce our stuff. Here are 5 of them - the last one is one of the biggest for me. 1. The cost of holding on. We were raised by our parents and grandparents and in their day items were expensive and space was cheap. It made sense in those days to hold onto stuff just in case you ever needed it. But today housing is expensive and items are cheap. It's hard to change a habit, but now we save much more by downsizing. 2. Keeping it in the family. For some reason we prefer to give things to those close to us. Again this was viable in the days of big families and lots of children to receive hand-me-downs. But these days we have smaller fa...

20 unplugged ideas

May 1-7 is Screen-Free Week . It's about spending time away from the screen and more time with each other - or doing things we love. It's a great chance to break the work-tired-watchTV-ads-shop-work cycle. This list of twenty alternative ideas is great for screen-free week. It's also a great reminder of things we could enjoy if we're shopping and spending less - and maybe working less and enjoying life more.