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21 Jun 2024 10:00
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  •   Home > News > Business > Features

    It Pays to Know how Numbers Grow

    The recent fuss over food price rises shows how little feel many New Zealanders have for the power of compounding numbers. And that lack of knowledge could harm them when borrowing and investing.


    When news broke that New Zealand grocery prices have risen 42.5 per cent since 2000, there was considerable concern expressed in the news media. Nobody, it seemed, bothered to work out that that was a rise of less than 4 per cent a year.

    In fact, the helpful CPI inflation calculator on the Reserve Bank’s website, www.rbnz.govt.nz, shows that food prices have risen 3.6 per cent a year since early 2000. And that’s a little less than wage growth. That means that for most people, food is cheaper than at the turn of the century – in terms of how many hours they have to work to buy it.

    Sure, food prices have grown considerably faster than transport – at 2.2 per cent a year since early 2000, and much faster than clothes prices, which have grown at a turtlish 0.4 per cent a year.

    But the item that should have copped the headlines is housing – with a growth rate of 7.8 per cent a year - although not for the reason you probably suspect. Contrary to popular belief, the housing component of the Consumer Price Index doesn’t include house prices.

    That seems odd at first – until you think about it. If you sell a house to me, you gain as many dollars as I lose. The two numbers net off to have a zero effect on total household spending.

    The government, instead, uses rents, renovation costs and the costs of building new houses in its calculations. And those costs have risen this decade more than twice as fast as food.

    But I’m straying from my main point, which is that relatively slow annual growth can add up considerably over ten years – and fast growth can balloon.

    Applying this to investing, growth of 5 per cent a year will turn $1,000 into nearly $1,650 in ten years. And, if you’re lucky and earn 10 per cent a year, $1,000 will grow into more than $2,700. That’s not far off tripling.

    On the borrowing side, your debt will of course grow at the same rate if the interest is 5 or 10 per cent. But if you have credit card debt at 20 per cent, and you make no repayments, $1,000 will grow to more than $7,250 in ten years. Running up credit card debt is a great way to keep yourself poor.

    There are several lump sum calculators on the internet that will help you make these calculations. But sometimes you can do it in your head, using a handy little trick called the Rule of 72.

    This applies if the value of something – let’s say a house – doubles.

    If it has doubled in ten years, divide 72 by 10 to get 7.2. Your house price has grown about 7.2 per cent a year. If the house doubles in six years, divide 72 by 6 to get 12. Your house price has grown about 12 per cent a year.

    You can also use the Rule of 72 if you know the return on something – let’s say a fixed interest investment. If it earns 8 per cent a year, divide 72 by 8 to get 9. That’s the number of years it will take for your money to double. Nifty!

    Note that the Rule of 72 is a mathematical approximation. It works pretty well for growth rates, interest rates or returns between 2 per cent and 15 per cent. Outside those limits it’s a bit rough.

    © 2024 Mary Holm, NZCity

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