Double Your Money: The Rule of 72The Rule of 72 is a quick and simple technique for estimating one of two things: Show
The rule states that an investment or a cost will double when: [Investment Rate per year as a percent] x [Number of Years] = 72. When interest is compounded annually, a single amount will double in each of the following situations:  The Rule of 72 indicates than an investment earning 9% per year compounded annually will double in 8 years. The rule also means if you want your money to double in 4 years, you need to find an investment that earns 18% per year compounded annually. You can confirm the rationality of the Rule of 72 as follows: Find factors on the FV of 1 Table that are close to 2.000. (The factor of 2.000 tells you that the present value of 1.000 had doubled to the future value of 2.000.) When you find a factor close to 2.000, look at the interest rate at the top of the column and look at the number of periods (n) in the far left column of the row containing the factor. Multiply that interest rate times the number of periods and you will get the product 72. To use the Rule of 72 in order to determine the approximate length of time it will take for your money to double, simply divide 72 by the annual interest rate. For example, if the interest rate earned is 6%, it will take 12 years (72 divided by 6) for your money to double. If you want your money to double every 8 years, you will need to earn an interest rate of 9% (72 divided by 8). Here's another way to demonstrate that the Rule of 72 works. Assume you make a single deposit of $1,000 to an account and wish for it to grow to a future value of $2,000 in nine years. What annual interest rate compounded annually will the account have to pay? The Rule of 72 indicates that the rate must be 8% (72 divided by 9 years). Let's verify the rate with the format we used with the FV Table: To finish solving the equation, we search only the "n = 9" row of the FV of 1 Table for the FV factor that is closest to 2.000. The factor closest to 2.000 in the row where n = 9 is 1.999 and it is in the column where i = 8%. An investment at 8% per year compounded annually for 9 years will cause the investment to double (8 x 9 = 72). Doubling Time Calculator (Click Here or Scroll Down) The Doubling Time formula is used in Finance to calculate the length of time required to double an investment or money in an interest bearing account. It is important to note that r in the doubling time formula is the rate per period. If one wishes to calculate the amount of time to double their money in a money market account that is compounded monthly, then r needs to express the monthly rate and not the annual rate. The monthly rate can be found by dividing the annual rate by 12. With this situation, the doubling time formula will give the number of months that it takes to double money and not years. In addition to expressing r as the monthly rate if the account is compounded monthly, one could also use the effective annual rate, or annual percentage yield, as r in the doubling time formula. Example of Doubling Time FormulaJacques would like to determine how long it would take to double the money in his money market account. He is earning 6% per year, which is compounded monthly. Looking at the doubling time formula, we need to consider that the 6% would need to be divided by 12 in order to come to a monthly rate since the account is compounded monthly. Given this, r in the doubling time formula would be .005 (.06/12). After putting this into the doubling time formula, we have: After solving, the doubling time formula shows that Jacques would double his money within 138.98 months, or 11.58 years. As stated earlier, another approach to the doubling time formula that could be used with this example would be to calculate the annual percentage yield, or effective annual rate, and use it as r. The annual percentage yield on 6% compounded monthly would be 6.168%. Using 6.168% in the doubling time formula would return the same result of 11.58 years. Alternative to Doubling TimeFor quick estimations of how long it takes to double the money on an investment, some may choose to use the rule of 72. The rule of 72 is found by dividing 72 by the rate of interest expressed as a whole number. For example, a rate of 6% would be estimated by dividing 72 by 6 which would result in 12 years. As stated, this is only an estimation as a 6% rate would take 11.90 years using the actual doubling time formula.
How long will it take money to double if it is invested at 5%?According to the Rule of 72, it would take about 14.4 years to double your money at 5% per year.
How do you calculate how long it will take to double your investment?The Rule of 72 is a simple way to determine how long an investment will take to double given a fixed annual rate of interest. By dividing 72 by the annual rate of return, investors obtain a rough estimate of how many years it will take for the initial investment to duplicate itself.
How long will it take an investment to double in value at 4% per year simple interest?If the interest per quarter is 4% (but interest is only compounded annually), then it will take (72 / 4) = 18 quarters or 4.5 years to double the principal. If the population of a nation increases at the rate of 1% per month, it will double in 72 months, or six years.
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