Interest Compounding - Using the Rule of 72 as a Handy Compass
By Acceler8now.com Investment Education Team
6th September, 2007
You most likely know about the rule of thumb. Well, the Rule of 72 is one rule of thumb you can find very useful in some computations relating to compound interest. Compound interest yields exponential growth in investment value and people who desire to tap into this power are likely to want to paint "what-if" scenarios to see how to achieve certain financial milestones. A compound interest calculator - and you can find free ones online - will help with the computations you want to do. There are also the algebraic formulas that you can apply if you are at home with your math. However, when neither of these options can work for you, there are some compound interest values you can derive with the Rule of 72 or other cousins of that rule. Let's see what.
DOUBLING YOUR INVESTMENT VALUE
That's right. That is the core business of the Rule of 72 - it helps you quickly approximate, sufficiently accurately, how long it takes for the value of your investment to double. Who doesn't want to see this? With this rule, you only need to know a rate of return and, presto, you can determine how long it will take you. If, for instance, you have a guaranteed 12% return from an investment and desire to estimate how long it takes to duplicate the value of the investment, simply divide 12 into 72. That gives 6, which is what it takes, at 12% per annum compounded return, for your investment to double. As shown in the chart below, approximations from this rule are very close, especially for not-very-large values of returns rate.
REQUIRED RETURNS RATE
The Rule of 72 easily does the reverse calculation of what return rate you should earn to double your investment, when you have chosen a period. If, for instance,
you have challenged yourself to grow your net-worth to a given value in 'x' years by doubling the value of the investment capital currently at your disposal - which is a worthy goal - you can easily apply the rule to determine the annual rate of return you must strive for (as a minimum), on that investment capital to double its value in that number of years. You have a current net-worth of N10 million out of which N8 million can be re-invested. You desire to double that amount to N16 million in 5 years to bring you to a total net-worth of N18 million. What rate of return must you generate for 5 years to achieve N18 million. Use Rule of 72 for a quick guide. Just divide 72 by 5 to derive the required rate of return. For individuals seriously working to build wealth, such snap calculation is clearly helpful, since you need visioning, a lot of planning and frequent recalculations, to achieve your goal.
CLOSING DOWN THE APPROXIMATION
The Rule of 72 gives results that closely agree with actual calculation. However, there are various possible scenarios, such as low, mid or high rate values, continuous or periodic compounding, etc. Variants of the rule that give even closer approximations in specific cases also exist. The Rule of 71, the Rule of 70 and the Rule of 69.3 can also be used. They work this same way. Rule of 71, for instance, will give the closest result for daily compounding. Well, you need to get familiar with using the rule of 72 first and you can go ahead to try the other variants.
ILLUSTRATION CHART
The chart below compares results from actual computations with those from Rule of 72 at various levels of return. As can be readily seen, each approximation is reasonably close. So when you need a quick check on how your wealth building effort can benefit from interest compounding, you may not engage in a labourious computation, especially if no calculator is handy. The rule will give you a good working approximation.
Comparison of Doubling Periods |
Rate of Return
% |
Number of years |
Rule of 72 |
Rule of 70 |
Actual |
4 |
18.00 |
17.50 |
17.67 |
5 |
14.40 |
14.00 |
14.21 |
6 |
12.00 |
11.67 |
11.90 |
7 |
10.29 |
10.00 |
10.25 |
8 |
9.00 |
8.75 |
9.01 |
9 |
8.00 |
7.78 |
8.04 |
10 |
7.20 |
7.00 |
7.27 |
11 |
6.55 |
6.34 |
6.64 |
12 |
6.00 |
5.83 |
6.12 |
|
|
