What is the 'Rule Of 72'
The rule of 72 is a shortcut to estimate the number of years required to double your money at a given annual rate of return.Â The rule states thatÂ you divide the rate, expressed as a percentage,Â into 72:
Years required to double investmentÂ = 72 Ã· compound annual interest rate
Note that a compound annual return of 8% is plugged into this equation as 8, not 0.08, giving a result of 9 years (not 900).
BREAKING DOWN 'Rule Of 72'
The rule of 72 is a useful shortcut, sinceÂ the equations related to compound interest are too complicated for most people to do without a calculator. To find out exactly how long it would take to double an investment that returns 8% annually, one would have to use this equation:
T = ln(2) / ln(1.08) = 9.006
Most people cannot do logarithmic functions in their heads, but they can do 72 Ã· 8 and get almost the same result. If it takes 9 years to double a $1,000 investment, then the investment will grow to $2,000 in Year 9, $4,000 in Year 18, $8,000 in Year 27, and so on. Conveniently, 72 is divisible byÂ 2, 3, 4, 6, 8, 9, and 12, making the calculation even simpler.
The unit does not necessarily have to be money: the rule could apply to any thing that grows, such as population. If Gross Domestic Product (GDP) grows at 4% annually, the economy will be expected to double in 72 Ã· 4 = 18 years. Also, in regards to fees that cut into investment gains, the rule of 72 can be used to demonstrate the longterm effects of these costs. A mutual fund that has 3% in annual expense fees will cut the investment principal in half over 24 years. A borrower that pays 12% interest on his credit cards will double the amount he owes in 6 years.
The rule can also be used to find the amount of time it takes for money's value to halve due to inflation. If inflation is 6%, then a given amount of money will be worth half as much in 72 Ã· 6 = 12 years. If inflation decreases from 6% to 4%, an investment will be expected to lose half its value in 18 years, instead of 12 years.
Adjusting For Higher Rates
The rule of 72 is reasonably accurate for interest rates between 6% and 10%. When dealing with rates outside this range, the rule can be adjusted by adding or subtracting 1 from 72 for every 3 points the interest rate diverges from 8%. So for 11% annual compounding interest, the rule of 73 is more appropriate; for 14%, it would be the rule of 74; for 5%, the rule of 71.
For example, say you have a 22% rate of return (congratulations). The rule of 72 says the initial investment will double inÂ 3.27 years. Since 22 â€“ 8 is 14, and 14 Ã· 3 is 4.67 â‰ˆ 5, the adjusted rule would use 72 + 5 = 77 for the numerator. This gives a return of 3.5, meaning you'll have to wait another quarter to double your money. The period given by the logarithmic equation isÂ 3.49, so the adjusted rule is more accurate.
Adjusting For Continuous Compounding
For daily or continuous compounding, using 69.3 in the numerator gives a more accurate result. Some people adjust this to 69 or 70 for simplicity sake.Â
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