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# LOUISE FAIRSAVE: Compound interest power

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Today, let us revisit the chart below: column 1 tracks the year of the investment return, column 2 presents the investment balance at the end of the related year when \$5 000 is invested at 10 per cent simple interest, column 3 represents the balances per year for the same investment at 10 per cent interest compounded annually, column 4 presents the difference in earnings between simple and compound earnings at 10 per cent and column 5 presents the results if the investment was compounded annually at 12 per cent.

This chart was used in explaining the interest rule of 72.  This rule applies to compound interest and says that “the rate of interest on an investment” R multiplied by ‘the number of years for your investment to double in value’ T equals 72:  R X T = 72  or: T = 72/R or R = 72/T.

As shown in the chart, column 3, at 10 per cent the \$5 000 investment would take approximately 72/10 =7.2 years to double.  Alternately, If the aim is to double the \$5 000 investment in 6 years, the return on the investment would have to be about 72/6 =12 per cent, reference column 5.

This rule also works in assessing the fall in value of money over time given the inflation rate. For example, \$5 000 will fall to half its value, \$2 500 in 24 (72/3) years at a 3 per cent inflation rate. Although inflation rates tend to vary over long periods of time, recognising the decaying effect of inflation on interest income is very important.

The accuracy of this rule fades more and more as interest rates move upwards of say 20 per cent.  However, the rule is exceedingly useful for quick assessments for typically everyday levels of interest rates. Computations required can mostly be done mentally.

The more accurate rule is the rule of 69.3, sometimes simplified to the rule of 70. The use of 69.3 would give more accurate results at any interest rate. However manipulated this number mentally is a greater burden. Yet, using the 69.3 rule is a shorter and a less complex approach than the exponential and logarithmic mathematical computation that would be required to get the exact result down to the last two decimal points.

Finally, the rule of 114 provides a similar quick assessment of the time needed to triple your money at a particular interest rate:  R X T = 114. I leave to you to check this rule using column 5. These rules allow you to assess the amazing effects of compound interest in powering your financial plans.