You will be able to divide 72 by a yearly rate to estimate how many years it takes money, or debt, to double.
Someone in a group chat says their investment returned 6% a year and asks how long it will take to double. Nobody has a spreadsheet open. One person guesses 16 years, because 100 divided by 6 is about 16. Another says it depends. The answer is about 12 years, and you can get it in your head in two seconds.
The trick is called the rule of 72: divide 72 by the yearly percentage rate, and the result is roughly the number of years it takes a sum to double with compounding.
72 divided by 6 is 12, so money growing at 6% a year doubles in about 12 years. At 9%, 72 divided by 9 is 8 years. At 3%, it is 24 years. At 12%, it is 6.
The guess of 16 years in the group chat came from treating the growth as simple interest, adding 6% of the original sum each year until the gains reach 100%. Compounding gets there sooner because each year's growth is on a larger balance, which you saw in lesson 2.1, Simple interest pays on what you put in, compound pays on what you earned.
The rule tells you how many years one doubling takes, and doublings stack. At 6%, S$10,000 becomes roughly S$20,000 after 12 years, S$40,000 after 24 and S$80,000 after 36. That makes it a quick way to sense what a long horizon does to a sum without working out any powers.
The rule is an approximation. The exact doubling time comes from logarithms, and in a spreadsheet the NPER function gives it to you, which you will use in Module 6. Here is how the shortcut compares with the exact answer at a few rates.
At 6%, the rule says 12 years and the exact figure is about 11.9. At 9%, the rule says 8 and the exact figure is about 8.04. At 15%, the rule says 4.8 and the exact figure is about 4.96. For rates between roughly 2% and 15%, the error is a few months at most, far less than the uncertainty in any real return.
Outside that range it drifts. At 1%, the rule says 72 years and the exact answer is about 69.7, so it overstates by more than two years. At 36%, the rule says 2 years and the exact answer is about 2.25, so at very high rates it understates. Use it as a first estimate, then calculate properly when a decision depends on the precise number.
You can turn the rule around. If you want a sum to double in a given number of years, divide 72 by the years to get the rate you would need.
To double in 10 years, you need about 72 divided by 10, which is 7.2% a year. The exact figure is about 7.18%. To double in 18 years, you need about 4% a year.
This is useful for testing a claim. If someone says an investment will double your money in three years, the rule tells you that means about 24% a year. You can then ask what kind of risk comes with a return like that, which Module 5 covers. A promise of doubling in a year or two is a warning sign, and the course Scam-proof your money looks at why.
Anything that compounds can be doubled with the same arithmetic, and that includes things you would rather did not grow.
Debt is the obvious one. A balance charged at 18% a year, a figure chosen as an example, doubles in about 72 divided by 18, which is 4 years, if nothing is repaid and interest keeps being added. The exact figure is about 4.2 years. That makes it easy to see why a balance left alone on a high-interest product gets out of hand.
Prices work the same way. If prices rise 3% a year, they double in about 24 years. Someone who is 30 today would, at that rate, be paying twice as much for the same groceries by the age of 54. Module 4 looks at inflation and what it does to the savings you hold.
The rule is useful only if you can do it without thinking, in a meeting with a banker, in a shop being offered an instalment plan, or reading a headline about returns. The way to get there is to try it on a handful of rates and check each estimate against the exact figure, so you see for yourself where it holds and where it slips.
Use the rule of 72 to estimate doubling time at 2%, 4%, 8% and 24% a year, then check each answer in a spreadsheet.
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