Rule of 72 is a shortcut formula to find out approximately in how many years the amount will double? Divide 72 by rate of return you will get an approximate number of years in which your money will double. For example, if you want to know how long it will take to double your money at 9% interest, divide 72 by 9 and you get 8 years. Let’s look at Rule of 72 in detail. The mathematics behind the rule of 72, How good approximation is Rule of 72? Other rules like Rule of 114 and 144.
How fast your money grows
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Rule of 72
Rule of 72 is regarded as of one of three essential personal finance topics to understand. The other two being compound interest and the time value of money.
Rule of 72 is a shortcut formula to find out approximately in how many years the amount will double?
The formula is simple: 72 / interest rate = years to double
1%, it will take 72 years for your money to double (72 / 1 = 72)
3%, it will take 24 years for your money to double (72 / 3 = 24)
6%, it will take 12 years for your money to double (72 / 6 = 12)
9%, it will take 8 years for your money to double (72 / 9 = 8)
12%, it will take 6 years for your money to double (72 / 12 = 6
Note that a compound annual return of 8% is plugged into this equation as 8, and not 0.08, giving a result of nine years (and not 900).
It also works backwards, so you can find the interest rate required for your money to double. For example, if you want to double your money in six years, just divide 6 into 72 to find that it will require an interest rate of about 12 per cent.
Rule of 72 comes in handy for mental calculations to quickly get an approximate value. If an investment promises an 8% annual compounded rate of return, it will take approximately (72 / 8) = 9 years to double the invested money.
it can compute the annual rate of compounded return from an investment given how many years it will take to double the investment.
The Rule of 72 applies to cases of compound interest, and not to the cases of simple interest.
The Rule of 72 could apply to anything that grows at a compounded rate, such as population, macroeconomic numbers, charges or loans.
- If the GDP(gross domestic product) grows at 6% annually, the economy is expected to double in 72 ÷ 6 = 12 years.
- A mutual fund that charges 2% in annual expense fees will reduce the investment principal to half in around 36 years.
- One who pays 12% interest on his credit card (or any other form of loans which is charging compound interest) will double the amount he owes in 6 years.
- If inflation is 6%, then a given purchasing power of the money will be worth half in around (72 ÷ 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.
Rule of 72 can be applied across all kinds of durations provided the rate of return is compounded.
- If the interest per quarter is 4%, then it will take (72 / 4) = 18 quarters or 4.5 years to double the principal.
- If the population of a nation increases as the rate of 1% per month, it will double in 72 months, or six years.
Mathematics behind Rule of 72
Using the formula of compound interest time to double for an interest rate of r per cent per period is
2P = P(1 + r)t
Rearranging it will give
where:t=Time to double, ln=Natural log function, r=Compounded interest rate per period, ≃=Approximately equal to
Rule of 72 is an approximation
The Rule of 72 is just an approximation. We could use 69.3 or 70, but 72 gives close results and has many more factors (2, 3, 4, 6, 12…) so for a mental shortcut, we go with 72.
The table below compares the numbers given by the Rule of 72 and the actual number of years it takes an investment to double.
| Rate | Actual Years | Rule of 72 | Rule of 70 | Rule of 69.3 |
|---|---|---|---|---|
| 0.25% | 277.605 | 288.000 | 280.000 | 277.200 |
| 0.5% | 138.976 | 144.000 | 140.000 | 138.600 |
| 1% | 69.661 | 72.000 | 70.000 | 69.300 |
| 2% | 35.003 | 36.000 | 35.000 | 34.650 |
| 3% | 23.450 | 24.000 | 23.333 | 23.100 |
| 4% | 17.673 | 18.000 | 17.500 | 17.325 |
| 5% | 14.207 | 14.400 | 14.000 | 13.860 |
| 6% | 11.896 | 12.000 | 11.667 | 11.550 |
| 7% | 10.245 | 10.286 | 10.000 | 9.900 |
| 8% | 9.006 | 9.000 | 8.750 | 8.663 |
| 9% | 8.043 | 8.000 | 7.778 | 7.700 |
| 10% | 7.273 | 7.200 | 7.000 | 6.930 |
| 11% | 6.642 | 6.545 | 6.364 | 6.300 |
| 12% | 6.116 | 6.000 | 5.833 | 5.775 |
| 15% | 4.959 | 4.800 | 4.667 | 4.620 |
| 18% | 4.188 | 4.000 | 3.889 | 3.850 |
| 20% | 3.802 | 3.600 | 3.500 | 3.465 |
| 25% | 3.106 | 2.880 | 2.800 | 2.772 |
| 30% | 2.642 | 2.400 | 2.333 | 2.310 |
| 40% | 2.060 | 1.800 | 1.750 | 1.733 |
| 50% | 1.710 | 1.440 | 1.400 | 1.386 |
| 60% | 1.475 | 1.200 | 1.167 | 1.155 |
| 70% | 1.306 | 1.029 | 1.000 | 0.990 |
Rule of 114, 144
Rule of 114 can be used to determine how long it will take an investment to triple
Rule of 144 will tell you how long it will take an investment to quadruple.
For example,
at 10% investment will
- double in 7.2 years (72/10)
- triple in about 11 years (114 / 10)
- quadruple in about 14.5 years (144 /10).
While it takes the interest rate divided into 72 to double, the interest rate divided into 144 quadruples!
That’s the influence of compounding.
The message of this story is: start to save early and try to save often
How long to become a Millionaire: Rule of 1.5 and 1,080,000
The Rule of 1.5, known as Felix’s Corollary allows you to estimate the future value of a series of payments, or an annuity, using the Rule of 72. It states that when the number of years invested times the interest rate equals 72, then the ending value will be 1.5 times the initial amount invested.
For example, you invest Rs 1000 a year for 8 years earning 9 per cent interest. The Rule of 1.5 says that after those 8 years, the money grows to 1.5 times the amount invested.
8 years x 9% interest = 72
Since Rs 1,000 was invested annually over a period of 8 years, then the total investment was Rs 8,000. Felix’s Corollary shows us that the ending balance will be Rs 12,000.
Rs 1,000 x 8X 1.5 = Rs 12,000
10,000 x 8 x 1.5 = 1,20,000
Using the Rule of 72, we know that whatever we have saved over the first 8 years will double over the next 8 years because 72 divided by interest rate of 9% equals 8.
1,000 per month at 9% interest it will take 24 years to be a millionaire
We need to do is decide how long it will take you to save 720,000 at a given interest rate. As 7,20,000 X1.5 = 10,80,000.
Say, with a saving of 90,000 per year you will need 8 years to acquire 720,000.
And at 9% annual interest, this would become Rs 1,080,000 over 8 years.
Other Rules for Investing
Emergency fund rule
Put away at least 3-6 months’ worth of expenses and ensure it is available at short notice.
100 minus your age rule
This rule is used for asset allocation. Subtract your age from 100 to find how much of your portfolio should be allocated to equities
Age 30: Equity : 70%, Debt : 30%
Age 60: Equity : 40%, Debt : 60%
Pay yourself first rule
Right from your first salary, put away a little for your retirement. Experts say 10% of your income should go into this. It is important to raise the amount as your income rises over the years.
4% withdrawal rule
How much money should you withdraw after retirement? Use the 4% rule to ensure that your investment survives.
Personal Finance Thumb Rules
Personal Finance Thumb rules
Related Articles:
Rule of 72 will show how to double your money. With investing just a bit over Rs 1,000 per month at 9% interest it will take 24 years to be a millionaire. What are the thumb rules you follow?
72/r gives approximate value.
But ln(2) ÷ln(1 + (r/100),gives the exact value. For interest rate 6%, the exact value is ln(2) ÷ ln(1.06) = 11.8956. As smart phone has calculator with ln and log , exact valuation is an easy task.