Rule 72 offers an easy method or way in which you can calculate the time frame mentally to get your money double. You might have come across many other useful formulas to calculate the time period in which your money can be doubled or you might think of situations how can I double my money? So, with the rule 72 formula, you might find answers to your questions and double your money too. S, let’s see what is this rule 72 for doubling your money.
What Is the Rule of 72?
Rule of 72 suggests you the best ways to invest money where you can determine how to double your money with a fixed annual rate of interest. And this can be done by dividing 72 by the yearly rate of return, the investor gets or has estimated the time for money doubling.
Thus, the rule of 72 tells you up the way in which you can double your money guaranteed in almost 7 years or say tells you does money double every 7 years and that too without involving much risk.
Rule of 72 is suggested to be used mentally as other various calculation formulas also do exist in excel and spreadsheets that tells you the time to double your money. So, by using the rule of 72 you might know does money double every 7 years or not. And if yes then how?
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Rule of 72 Formula:
The formula to calculate does money double every 7 years is as follows:
- Years to Double = 72 / Interest rate
Where in the above formula to determine does money double every 7 years:
- Interest Rate = Rate of return on an investment
As for reference, you can see that:
- With 6 percent ROI: You get 6 % return if you want to know the time by which your money doubles you will divide 72 by 6 percent as follows:
Years to Double = 72 / Interest rate
Time money doubles = 72 / 6 % = 12
Thus, by the 12 years, your money will get double with a 6 percent return on your investment.
- With 7 percent ROI: You get 7 % return if you want to know the time by which your money doubles then you will divide 72 by 7 percent as follows:
Years to Double = 72 / Interest rate
Time money doubles = 72 / 7 % = 10.2
Thus, by 10.2 years your money will get double with a 7 percent return on your investment.
- With 8 percent ROI: You get 8 % return if you want to know the time by which your money doubles then you will divide 72 by 8 percent as follows:
Years to Double = 72 / Interest rate
Time money doubles = 72 / 8 % = 9
Thus, by the 9 years, your money will get double with an 8 percent return on your investment.
- With 9 percent ROI: You get a 9 % return if you want to know the time by which your money doubles then you will divide 72 by 9 percent as follows:
Years to Double = 72 / Interest rate
Time money doubles = 72 / 9 % = 12
Thus, by the 12 years, your money will get double with a 9 percent return on your investment.
- With a 10 percent ROI: You get a 10% return if you want to know the time by which your money doubles then you will divide 72 by 10 percent as follows:
Years to Double = 72 / Interest rate
Time money doubles = 72 / 10 % = 7.2
Thus, by the 7.2 years, your money will get double with a 10 percent return on your investment.
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Calculating the Rule of 72:
Here we will tell you how to multiply money by calculating the rule of 72:
We see that if the rate of return on investment or interest rate is 8 percent than the amount will get double as per rule 72 as = 72 / 8 = 9 years. Here we use the compound annual return of 8 % but have written down it as 8 % and not as 0.08 by which we get 9 years as the time period to double the money.
Therefore, the above rule 72 formula is developed by using a basic sort of the original logarithmic calculation and using some complex functions in that logarithmic calculation by taking the natural log of numbers.
Therefore, the exact time to calculate doubling time for an investment that earns out a compounded interest rate or return on investment of r % per period is noted down as follows:
- T = ln ( 2 ) / ln ( 1 + ( r / 100 ) )
OR
- T = ln ( 2 ) / ln (1 + (r %) )
Where in the above equation time to calculate doubling time for an investment:
- T = is referred to as Time to double
- ln = is referred to as the Natural log function
- r = is referred to as the Compounded interest rate per period
- ≃ = is referred to as Approximately equal to
So, you can use the above discovered formula how much actual time will it take for an investment of 8 % annually to get double as follows:
T = ln ( 2 ) / ln ( 1 + ( 8 / 100 ) ) = 9.006 years
9.006 years found by the above exact formula is much close by to the approximate value obtained by (72 / 8) = 9 years
As by now you might have understood that log functions are not handy and easy option to do mental calculations quickly. Therefore, we use the rule of 72 formula that makes use of the factor of 72 and a much easier option and delivers approx. the same result as the longer actual log formula.
Rule of 72 and Natural Logs:
As you know by now that rule of 72 uses natural logarithms. Where you might also be knowing that the logarithm is the opposite of a power; for example, the opposite of 104 is log base 10 of 10,000.
So,
- Rule of 72 = ln ( e ) = 1
where:
- e = 2.718281828
Note: As you know in mathematics e is a famous irrational number just like we use pie as an e is a famous irrational number. And the value of e is 2.718281828.
And, the TVM (time value for money) formula is as:
- Future Value = PV × ( 1 + r ) n
where:
- PV = Present Value
- r = Interest Rate
- n = Number of Time Periods
- Step 1: And if you want to know does money double you mark down the future value as 2 and mark down the present value as 1 in the above formula as follows:
2 = 1 × ( 1 + r ) n
- Step 2: And by simplifying the above equation you get:
2 = ( 1 + r ) n
- Step 3: And in order to remove the exponent in RHS or right side of the equation we will take log both the side as follows in the next step on both the side:
ln ( 2 ) = n × ln ( 1 + r )
- Step 4: Simplifying the equation, we get,
ln ( 2 ) = r × n
- Step 5: Now, quoting the value of The natural log of 2 which is 0.693
ln ( 0.693 ) = r × n
- Step 6: Now, dividing both sides by the interest rate, you get the following:
0.693 / r = n
- Step 7: Now, expressing this as a percentage you get the formula as follows:
69.3 / r % = n
Rule of 72 Examples:
We have quoted the following examples that will help you understand how to double your money?
Example 1: If you capitalize a sum of money at 6 % interest per year, how long will it take to double your money or investment?
Solution: Using the 72 rule formula as:
- R * t = 72
Where in the above formula,
- R = interest rate per period as a percentage
- t = number of periods
Therefore, putting the values as follows:
T = 72 / R = 72 / 6 = 12 years
Example 2: what interest rate would double your money in 5 years?
Solution: Using the 72 rule formula as:
- R * t = 72
Where in the above formula,
- R = interest rate per period as a percentage
- t = number of periods
Therefore, putting the values as follows:
R = 72 / t = 72 / 5 = 14.4 %
Example 3: If you invest a sum of money at 0.5% interest per month, how long will it take to double your money or investment?
Solution: Using the 72 rule formula as:
- R * t = 72
Where in the above formula,
- R = interest rate per period as a percentage
- t = number of periods
Therefore, putting the values as follows:
T = 72 / R = 72 / 0.5 = 144 months
Note: here, in the above example r, which stands for the rate of interest is given in months therefore we have obtained our answer of the period in which money gets double in months only.
Example 4: How can you double up your money in 1 year?
Solution: For doubling the money in a year with real account rule:
- Years to Double = 72 / Interest rate
Where in the above formula to determine does money double up:
- Interest Rate = Rate of return on an investment
Interest Rate = 72 / 72 = 1 year
Thus, you need to search for an interest rate on investment offered at 70 to 72 % as to double your money.
Usage of the rule of 72:
There are many cases where you can use the 72 rule in your life for calculating the value of investments and their doubling up time. Thus, while investing you can use the rule in the following cases of investments which users find profitable to invest and grow their money in:
- Stock market: If you want to gain interest over the shortest period then stock market option where a good return on investments or ROI is yielded by investor although there also exist risk factors too. So, the stock market option is one of the best ways to invest money.
You can also invest in stocks using an employer-sponsored 401(k) plan where investors have seen 401k doubles every 7 years too. So, there’s a high chance of profit.
- Bank fixed deposits: You can also use bank FDs to deposit money and earn interest on them although it is a slow process that needs time and patience by an investor. Here, an interest rate of around 8 % to 9 % can be obtained.
- Mutual funds: Mutual funds are also the best way to invest money and with in 6 to 7 years you can be estimated to get double the money you invested in. Although, here also market risk factor is there so you should know the market as well as analyze the market thoroughly before investing in the mutual funds’ option.
How to double your money in a day?
To double up your money in a day you can opt for various investment options such as follows:
- Investing in the Stock Market
- Investing in the Real Estate Sector
- Lend Your Money to gain interest charged
- Open a savings account
Rule 72 Calculator:
You can use the time to double money calculator to calculate and save your time and avoid any mistake while you calculate and invest your money to know does money double every 7 years. You can use various rule 72 calculators available online for this purpose.
How Often Should Your Money Double?
The amount of time that is prerequisite to double up the money can be estimated by dividing 72 by your rate of return. As, if you have invested a money or are willing to invest money at an interest rate of 10 % then your money will get doubled up as T= 72 / 10 = 7.2 years.
How Can I Double My Money In A Year?
In order to know this, you need to divide 72 by your expected annual rate, which will provide you with the number of years it will take to double your money.
What Will 100k Be Worth In 20 Years?
By the end of 20 years, your savings with 100k will have matured to $ 320,714. As you will receive $ 220,714 as an interest on 100k amount invested 10 years before.
How Many Years The Money Will Double In The Bank?
To calculate the doubling time taken for money in the bank firstly you need to know the Annual Interest Rate offered by the bank. Then, you need to divide 72 by the Annual Interest Rate which the bank offers that will provide you will the resultant time your money gets doubled. As, if the bank offers 8 % as an annual interest rate then:
T = 72 / R = 72 / 8 % = 9 years. So, it will take 9 years for money to get double if bank offers 8 % as annual interest rate.
How Much Will $500 Be Worth In 20 Years?
By the end of 20 years, your savings with $ 500 will have matured to $ 1,604. As you will receive $ 1,104 as interest on the $ 500 amount invested 10 years before.
Why Does The Rule Of 72 Work?
Using the rule of 72 allows you to have a solid idea of when your investment would double just from the investment rate. Very conveniently, the number 72 divides cleanly into 1, 2, 3, 4, 6, 8, 9 and 12, allowing for a quick and simple division problem instead of your usual compound interest problem.
Is The Rule Of 72 Accurate?
The Rule of 72 applies to compounded interest rates and is reasonably accurate for interest rates that fall in the range of 6% and 10%. The Rule of 72 can be applied to anything that increases exponentially, such as GDP or inflation; it can also indicate the long-term effect of annual fees on an investment’s growth.
What Are The Limitations Of The Rule Of 72?
The main limitation of the Rule of 72 is that it assumes a constant interest rate, which may not be the case in the real world. In reality, interest rates can fluctuate, which can impact the accuracy of the Rule of 72 calculation.
Conclusion:
Rule 72 offers an easy method or way in which you can calculate the time frame mentally to get your money double. You might have come across many other useful formulas to calculate the time period in which your money can be doubled or you might think of situations how can I double my money? Rule of 72 is such a formula you can use to calculate the time period in which your money can get doubled.
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