# Compound Interest: Best Friend or Worst Enemy?

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I first realised the power of compound interest when I was watching an episode of Futurama. The basic storyline was that someone had put \$1 into a bank account 500 years earlier and that this savings account now formed part of an inheritance.

That’s probably not something that gets people very excited. But it suddenly becomes exciting if you throw compound interest into the mix. Assuming a conservative annual interest rate of 5% (see the highest-paying savings accounts in Australia), how much do you think this initial \$1 investment would be worth after 500 years? \$10, \$1000, \$1 million, more?

### The Mind Trick

Actually, the answer amounts to about \$39 billion! Yes, that’s correct, not millions but billions of dollars. And that was based on a single dollar!

Unbelievable isn’t it? It really is unbelievable – And that is because human minds have difficulty processing exponential growth. It is hard for us to understand this type of growth and banks take advantage of that.

Indeed, our difficulty with this type of math explains why many people don’t bother with savings accounts – They don’t think they would earn very much.

It also explains why a vast majority of us take on debt without understanding (or even completely disregarding!) the total cost of borrowing.

Although 500 years is obviously an unrealistic time horizon, the impact of compound interest is significant even over the standard 25 or 30 year interest periods. And those are common mortgage durations. Scary? It should be.

We have linear minds, so thinking about this issue isn’t going to help you understand it. When it comes to finance, it’s best to stop doing ‘mental maths’ and start using calculators and spreadsheets! That’s what they are there for. To help simplify complexity and help us engage in better planning.

If you do start using these tools, you will better understand the financial implications of your decisions and will be able to save a lot of money.

I’ll even make it easy for you: I will give you all the formulae you need to be financially smart and have more robust discussions with your banker.

The maths are correct – Incredible as they may seem. I’ve heard my friends say “No, that’ can’t be right!” too many times to recount. But, sadly, it is right.

### The Compound Interest Formula

Assuming an initial amount $A_0$ is invested in a bank account paying out an annual interest rate $r$, the final amount $A_n$ obtained after $n$ years is:

$A_n = A_0 (1 + r)^n$

Below is a table with sample numbers for a range of initial capital and maturities where we assume an interest rate of 5% per annum, net of inflation.

0 Years
5 Years
10 Years
15 Years
20 Years
25 Years
\$100,000
\$127,628
\$162,889
\$207,893
\$265,330
\$338,635
\$250,000
\$319,070
\$407,224
\$519,732
\$663,324
\$846,589
\$500,000
\$638,141
\$814,447
\$1,039,464
\$1,326,649
\$1,693,177
\$750,000
\$957,211
\$1,221,671
\$1,559,196
\$1,989,973
\$2,539,766

This table demonstrates that over 25 years you could more than triple your capital with a compound interest of 5% per year. And if you could make additional regular deposits on top, your savings account would grow even faster.

Of course, there is a darker side to finance. If you take out a 25-year mortgage at 5%, you could end up paying more than twice the value of the house. I know all mortgage holders will argue about how property prices always go up, how renting means throwing money away, etc… but this simply isn’t true.

For now, just think about whether you would be happy paying twice the price for your house. I guess not. But I assure you, the banker is laughing all the way to the bank!

There are good and bad sides to compound interest. That depends on whether you have savings or debt. If you have savings and are earning interest, your capital will grow faster than you could imagine. If you have debt and are paying interest, you will end up paying much more money than you initially thought.

Most of the time, people taking out a mortgage won’t acknowledge that they are being ripped off. “If it’s so bad, why would everyone else be doing it, right?”

In the beginning, I tried to argue with my friends. However, I soon learnt that our opinions will never converge. Rationality doesn’t feature strongly in home ownership. People want to own houses for all sorts of reasons – One of them is social convention.

We’ve been told since we were very young that home ownership is important, something to strive for in life, something to show others that ‘we’ve made it’.

In the end, I gave up trying to convince closed-minded people to pay off their mortgages early. Why? Because if there were no financially naive people taking out mortgages at a 7% interest rate, I would not be able to earn 5% risk-free interest as I currently do…

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#### Monkey Master

My wife and I are currently living in Sydney, Australia. We plan on becoming financially self-sufficient in 2015 so we can retire at 35. We are regular working people, trying to be smart about saving money and generating passive income. I want to share with you how we reached that decision and how we are planning towards financial independence. Continue Reading.
Contact: monkeymaster@monkeyism.com