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Compounding Returns

November 26, 2014

This week we’ve been discussing personal finance. We’ve been through superannuation, and the core rules for building wealth. Today I want to discuss a crucial tenet of anything to do with finance – compound interest and compounding returns.

What is Compound Interest and Why Does it Exist?

Compound interest is essentially ‘interest on interest’. Imagine you have $1000 in a bank at 6% interest and interest is paid annually. After one year you have $1060 dollars. You earned $60 interest. The next year, however, you have $1123.60. You earned $63.60 dollars interest. So, the power of compound interest meant you got an extra $3.60 extra. Now, lets imagine you invested for 50 years. If not for compound interest you’d simply earn 50*60 = $3000 interest. With compound interest, however, you earn $17420.15 interest. That is over 5 times the interest!

This is also a good time to note that in the 50th year the interest was $982.65 greater than the simple interest of $60. Why such a difference? Because compound returns are greatest the longer they are left. At first it was $3.60 extra – not much. But over time that difference grew and grew and grew, and the extra interest became massive. In essence, compound returns give extremely good returns over longer time scales.

Simple-vs-Compound-Interest

Why is this so?

Mathematically speaking, compound interest is akin to an exponential graph (y=a**x), whereas simple interest is a linear function (y = mx + b form) . For compound interest, A = P(1+r/n)**nt, wherein n= the number of times per year interest is compounded. Obviously, given the power of compound interest, the more often an amount compounds the greater it will be. That’s why banks compound daily…

2000px-Compound_Interest_with_Varying_Frequencies.svg

Simple interest is simpler, A = P(1+rt). Note how this is a linear function.

Thats our mathematical explanation. As to why we have interest in the world… lets leave that interesting history for another time.

Compound Interest Matters!

Compound interest matters for 2 reasons – it can greatly maximise your income over time, or lead to rising costs.

The good news for you is that compound interest is simple to understand. You don’t need an MBA to understand it, so you can make it work for you if you persist. Also, time is on your side when depositing money with compound interest. If you can save a few dollars now, the return down the road is much greater. Your cup of coffee today might be worth a chair many years down the road. Your $1000 worth a holiday down the track. Sacrifices today reap rich rewards in the future.

However, compound interest is a double edged sword! Banks charge compound interest, and regularly too for a reason – it maximises their profits, and makes you pay more. Understand that banks and credit card companies want you to make only the “minimum repayment” because it allows the principal to stay large. Remember how I said earlier that compound interest reaped you the greatest returns over longer periods of time? Thats what a minimum repayment does – it elongates the repayment period to maximise the compound interest and repayments. Instead, when paying back interest, you want to fight against the curve and really, really hammer the initial amount compounding. See below.

graph_01

Compound interest can be scary. Use your awareness to maximise your savings, and minimise your repayment.

The Importance of Different Interest Rates

We’ve talked about the impacts of compound interest, and how over time the importance of compound interest increases. This can be extended to say that the differences in interest charged become greater over time because of ‘interest on interest.’

If you take the following from my superannuation article below (substitute ‘fees’ and think of a 1% difference in interest):

“A 1% difference in fees now could make up to a 20% difference to your retirement investment in 30 years, so it’s worth thinking about.” – Supersavvy

If you’re an 18 year old, we’re talking 50 years here – an even bigger difference! 0.99**50 (ie. 0.99 to the power of 50) = 0.605 .

That means a 1% difference in fees for 50 could reduce YOUR savings by nearly 40% for retirement. Thats the power of compound interest.

A 2% difference in fees is even greater. 0.98**30 = 0.545 . 0.98**50 = 0.364. What does that mean? You get 2% difference in fees over 30 years and you lose 44.5% of your retirement savings. Over 50 years you lose 63.6% of your savings.

The point is that differences in rates count. It doesn’t even have to be compounding to bite. If you owe $500,000 to the bank then even a 0.25% difference in interest would be worthy $1250 over one application of interest:

$500,000 * 1.05 = 525,000

$500,000 * 1.0525 = $526,250

$1250 dollars. Thats about the average earning for a week, isn’t it?

Normally I think playing hardball in negotiations, war and other areas can potentially lead to bad results. However, when looking at interest repayments I recommend you fight for every basis point in that rate, and search around for the lowest loan rate and highest savings rate! (If not investing in stocks for returns). Your home repayments are going to be the biggest cost in your life. Fight for every single tiny difference in that loan rate. Over 25 years on a million dollars, it makes a serious difference.

And that difference is a big one… thanks to compound interest.

Conclusions

My simple advice to you is to be aware of compound interest. Never underestimate its power. We are easily tempted to think in terms of the present, yet compound interest shows how the burden or harvest later down the road is immeasurably greater. Act wisely.

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