Investment Sums

If you read an advanced-level textbook on economic, the mathematics involved may make your eyes water.  That’s OK because while many advanced economists are also successful investors, there are also many successful investors who only have a basic knowledge of economics and its associated maths.  In fact, these days, as an investor, the only maths you really need to understand is percentages, which you probably did without even thinking about it when you were at school.  If, however, you’re maths has become a little rusty since then, here is a brief guide to doing your investment sums.

Understanding percentages

The key to understanding percentages is to think of the literal meaning of the term “per cent” or “per one hundred”.  Everything to do with percentages revolves around the idea of a quantity being measured against one hundred.

The super-easy way to calculate percentages

For the really mathematically-challenged, the simplest way to deal with calculating percentages is simply to calculate 1% of anything and then take it from there and the simplest way to calculate 1% of any figure is just to divide it by 100, in other words to move it two decimal places to the right.

For example, if you take 100 and move it two decimal places to the right, you get 1.  This method also works with numbers which are closer to, or even beyond, the decimal point.  For example, if you wanted to work out 1% of 1, you could still move it two decimal places to the right to give 0.01 and if you wanted to work out 1% of 0.01 then you’d just move it another two decimal places to the right, giving 0.0001 and so on.  Once you have this 1%, you can then use it as the basis for any other calculation you want.

Let’s say you have a £500 bond with a term of one year and an interest rate of 3% per annum.

500/100=5 so 1% of 500 is 5 so 3% of 500 is 15 so you will receive £515 back at the end of the year.

Alternatively, if you were being charged 3%, you would subtract the £15 and be left with £485.

Percentages and investment risk (including taxes)

Risk is a part of investment, but all risks should be calculated against benefits.  Most investors have probably grasped that in principle, but successful investors need to go beyond principle and put it into practice.  Here’s the basics of how to do that.

Let’s say you have an investment which offers a return of 10% per annum, but you calculate that there is a risk of you losing 5% of your money per annum.  So, as we have already demonstrated, for every £100 you invest, you could either end up with £110 or £95.

Now, let’s say that your first year is a bad year and you wind up with £95.  How long will it take you to get back into profit?

To calculate this, divide the percentage lost by the amount needed to make 100% and then multiply the result by 100, hence 5/95*100 = 0.053, so you would need to make 5.3% profit to make up for your initial 5% loss.  In this instance, if your next year was a good year, this would be easily achievable, but what if you had a second bad year?  This time you would be starting with £95 so your loss would be £4.75 to leave you with £90.25.  This is 9.75% down on your initial £100 so the sum would be 9.75/90.25/100=10.8%, hence even if your third year was a good year, you would actually still be down on your initial investment.

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