Rule of 72 is a basic investment rule that estimates the amount of time it will take to double your money. It is generally used as a simple and straightforward method for estimating an investment’s doubling time or halving time. In this article, we will go through the application of the Rule of 72.
How to apply the Rule of 72
These rules apply to exponential growth and decay respectively, and are therefore used for compound interest as opposed to simple interest calculations.
Years to double = 72 / Interest Rate
Take the percentage of interest on your money and divide it into 72.
- For example, an interest rate compounded at 9% percent would double in eight years (72/9 = 8).
- If medical fees increase at 8% per annum, the “rule of 72” gives 72/9 = 8 years later, your medical bill will double; an exact calculation gives 8.0432 years. After another 8 years, you will need to pay 4 times of the medical bill compared to present situation.
- When your unit trust consultant told you that a particular fund gives 100% return in 6 years. You roughly know that the fund’s annualized 72/6 = 12% return per annum.
- If inflation rates go from 2% to 3%, your money will lose half its value in 36 or 24 years.
- A share you bought 8 years ago is only worth 1/4 of its previous value. Using rule of 72 twice, the share shrinks at a rate of 18%p.a. (For the initial 4 years, it falls to half of its value. Wait another 4 years, it falls further to only a quarter remaining)
When to use the Rule of 71, 70 and 69.3
The rule of 72 provides a good approximation for annual compounding, and for compounding at “typical rates” (from 6% to 10%). But there are situation where other rules will give more accurate answer.
- low rates – for lower rate than 6%, Rule of 69.3 will give a better result than Rule of 72.
- daily compounding – Since daily compounding is close enough to continuous compounding, for most purposes 69.3 – or 70 – is used
- higher rates – a bigger numerator would be better (e.g. for 20%, using 76 to get 3.8 years would be only about 0.002 off, where using 72 to get 3.6 would be about 0.2 off). This is because, as above, the rule of 72 is only an approximation that is accurate for interest rates from 6% to 10%. Outside that range the error will vary from 2.4% to ?14.0%. For every three percentage points away from 8% the value 72 could be adjusted by 1.
Felix’s Corollary provides a method of approximating the future value of an annuity (a series of regular payments), using the same principles as the Rule of 72. The corollary states that future value of an annuity whose percentage interest rate and number of payments multiply to be 72 can be approximated by multiplying the sum of the payments times 1.5.
As an example, 12 periodic payments of $1000 growing at 6% per period will be worth approximately $18,000 after the last period. This can be calculated by multiplying 1.5 times the $12,000 of payments. This is an application of Felix’s collorary because 12 times 6 is 72. Likewise, 8 periodic thousand dollar payments at 9% will result in 1.5 times the $8000, or $12,000.
The millionaire’s estimation is a simple savings calculator, posing the question “How much must I save per year to have saved $1,080,000?” Of course, the annual interest rate is a factor. In the original challenge, the number $1,080,000 was chosen due to its multiplicative relation to the number 72.
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Using Felix’s corollary, one can estimate that by saving two-thirds of the total, in periodic deposits, the interest will take care of the rest (since 1.5 times two-thirds will equal the desired goal). So the goal becomes to set aside $720,000 in equal periodic deposits, such that it grows to approximate the target amount of $1,080,000.
If you want to be a millionaire in 12 years, just save $60,000 a year in an investment vehicle that gives you 6% a year.
If you want to be a millionaire in 6 years, just save $120,000 a year in an investment vehicle that gives you 12% return per annum.
Summary for Action
The ‘Rule of 72’ is a simplified way to determine how long an investment will take to double, given a fixed annual rate of interest. I bet you don’t want to bring your financial calculator wherever you go. Just apply the Rule of 72 to quickly make a rough estimate of a particular investment. Try estimate the route your friends or family member can become a millionaire using the Felix’s Corollary and the Rule of 72.