Rule of 70 is a short-cut method of an economy’s growth accounting which tells us that if an economy’s annual growth rate is g, its output/GDP will double in 70/g years. Show For example, if an economy grows by 2.3% constantly, rule of 70 tells us that its total production will double in 70/2.3 years i.e. in 30.43 years. The formula for rule of 70 can be written as follows: $$ \text{t}=\frac{\text{70}}{\text{g}} $$ Where t is the time it takes the economy to double and g is the constant percentage growth expected in future. DerivationIf an economy grows at a constant rate annual rate g, the value of its gross domestic product (GDP) after t years is given by the following formula: $$ \ {\rm \text{GDP}} _ \text{t}={\rm \text{GDP}} _ \text{0}\times{(\text{1}+\text{g})}^\text{t} $$ Now, let’s divide both sides by GDP0: $$ \frac{{\text{GDP}} _ \text{t}}{{\text{GDP}} _ \text{0}}={(\text{1}+\text{g})}^\text{t} $$ If an economy doubles over a period, the rate of GDPt to GDP0 would be 2. Substitute this in the equation: $$ \text{2}={(\text{1}+\text{g})}^\text{t} $$ Let’s take natural log of both sides of the equation: $$ \ln{\text{2}}=\ln{{(\text{1}+\text{g})}^\text{t}} $$ Natural log of 2 roughly equals 0.70 $$ \text{0.7}=\text{t}\times\ln{(\text{1}+\text{g})} $$ Since ln (1+g) is equal to g $$ \text{0.7}=\text{t}\times \text{g} $$ We need to multiply and divide by 100 so as to bring the expression in percentages. $$ \text{t}=\frac{\text{0.7}}{\text{g}}\times\frac{\text{100}}{\text{100}}=\frac{\text{70}}{\text{g}} $$ ExampleUS GDP in 2017 was $18.09 trillion (2016: $17.66 trillion) representing annual growth rate of 2.43%. Using rule of 70, we estimate that if the US economy continues to grow at 2.43%, it will double in 28.80 years. $$ \text{t}=\frac{\text{70}}{\text{2.43}}=\text{28.80} $$ Now, let’s find out how accurate rule of 70 is by finding the project value of US GDP in 28.80 year using the formula for compound annual growth rate: $$ {\rm \text{GDP}} _ \text{t}={\rm \text{GDP}} _ \text{0}\times{(\text{1}+\text{g})}^\text{t}\\=\text{\$18.09 trillion}\times{(\text{1}+\text{2.43%})}^{\text{28.80}}=\text{\$36.12 trillion} $$ Since the double of $18.09 trillion is $36.18 trillion, our estimate of $36.12 trillion is very close. Rule of 70 can be applied regardless of the absolute value of gross domestic project. It means that the rule can be applied to any economy. The term “Rule of 70” or also known as doubling time, refers to the total time required to double the quantity or value (we have taken money). It simply means that if all other factors remain constant, then in how much time it will take to double our money or investments or profit. For instance, suppose if we have invested $100 at a growth rate of 5% per annum, then in how much time our money invested has doubled, i.e., becomes $200. The above-said method is also known as doubling time or in simple time required to double the amount. Table of contents
Rule of 70 FormulaIn this article, we will focus on the formula for calculating the Doubling timeDoubling TimeThe doubling time formula measures the time taken by an investment to become twice its present value. Doubling Time = ln 2 / [n * ln (1 + r/n)]; where r is the rate of return and n is the number of compounding period per year.read more using the rule of 70, which is expressed as the division of 70 by the % of growth rate. Mathematically, it is represented as: Doubling Time = 70 / % of Growth Rate For the calculation of growth rateCalculation Of Growth RateThe Growth rate formula is used to calculate the annual growth of the company for a particular period. It is computed by subtracting the prior value from the current value and dividing the result by the prior value.read more, we need to apply the following formula: Growth Rate (per annum) = (Amount Received on maturity subtracted by Amount Invested) divided by Amount invested thereafter multiplied by 365 days / 12 months divided by period of investment. Mathematically it can be represented as: Growth Rate = (Amount Received – Amount Invested) / Amount Invested Multiplied by 365 Days or 12 Months / Period of Investment * 100 (as always in %)  You are free to use this image on your website, templates, etc., Please provide us with an attribution linkHow to Provide Attribution?Article Link to be Hyperlinked ExplanationThe equation for Rule of 70 can be derived by using the following steps: Step 1: Firstly, determine the number of investments and the period of investment. Step 2: Then, calculate the return on investment, which we got by subtracting the amount invested from the amount received on maturity called “Return.” Step 3: Then, determine the period of investment in which we got returns or capital appreciations, i.e., the period from the date of investment to maturity called “T.” Step 4: By using the above-mentioned formula for calculating the growth rate, calculate the growth rate of the investment called “G.” Step 5: Finally, by using the above-mentioned formula, we can easily calculate Doubling Time. Doubling time, as calculated in step 4. Doubling Time = 70 / by % of Growth Rate (g) Calculate Doubling Time using Rule of 70Let’s see some simple to advanced examples to understand it better. You can download this Rule of 70 Formula Excel Template here – Rule of 70 Formula Excel Template Example #1Suppose Mr. A has invested $100000 on the first day of the month in equity-oriented funds for a period of 3 months. At the time of maturity, Mr. A has received a sum of $150000. Now Mr. A wants to know the doubling time assuming all other factors in which business operates remain constant. Solution: Use the given data for the calculation of the rule of 70. Then for calculation of growth rate, the following steps are to be taken: Amount Earned on Investments = Amount Received on Maturity – Amount Invested
Now, Calculation of Doubling Time can be done as follows,
Doubling Time will be –
Example #2Suppose Mr. A has invested $100000 on the first day of the month in equity-oriented funds and has earned a dividend on these investments amounting to $5000. He has also invested in 10% debenturesDebenturesDebentures refer to long-term debt instruments issued by a government or corporation to meet its financial requirements. In return, investors are compensated with an interest income for being a creditor to the issuer.read more of PQR Inc., amounting to $500000. The period of both investments is 6 months. At the time of maturity, Mr. A has received a sum of $150000 from the equity-oriented fund and $520000 from 10% debentures. Now Mr. A wants to know the doubling time assuming all other factors in which business operates remain constant, and PQR Inc. pays interest on a half-yearly basis. Solution: Use the given data for the calculation of the rule of 70. Amount Earned on Investments = Amount Received on Maturity – Amount Invested
Other incomes earned from investments:
Growth rate (G) can be calculated by using the above formula:
Calculation of Doubling Time can be done as follows,
Doubling Time will be –
Rule of 70 CalculatorYou can use this rule of 70 calculators. % of Growth RateDoubling Time Doubling Time = 70 / % of Growth Rate70 / 0 = 0 Relevance and Uses
Recommended ArticlesThis has been a guide to the rule of 70. Here we discuss how to calculate doubling time using its rule of 70 formula along with examples, a calculator, and a downloadable excel template. You can learn more about financial analysis from the following articles –
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