Post by xray on Dec 9, 2022 14:31:34 GMT
Investopedia
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The Rule of 72: What It Is and How to Use It in Investing
By CAROLINE BANTON
Updated August 17, 2021
Reviewed by ANDY SMITH
Fact checked by SUZANNE KVILHAUG
What Is the Rule of 72?
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 the Rule of 72 Works
For example, the Rule of 72 states that $1 invested at an annual fixed interest rate of 10% would take 7.2 years ((72/10) = 7.2) to grow to $2. In reality, a 10% investment will take 7.3 years to double ((1.107.3 = 2).
The Rule of 72 is reasonably accurate for low rates of return. The chart below compares the numbers given by the Rule of 72 and the actual number of years it takes an investment to double.
Rate of Return Rule of 72 Actual # of Years Difference (#) of Years
2% 36.0 35 1.0
3% 24.0 23.45 0.6
5% 14.4 14.21 0.2
7% 10.3 10.24 0.0
9% 8.0 8.04 0.0
12% 6.0 6.12 0.1
25% 2.9 3.11 0.2
50% 1.4 1.71 0.3
72% 1.0 1.28 0.3
100% 0.7 1 0.3
Notice that although it gives an estimate, the Rule of 72 is less precise as rates of return increase.
The time value of money (TVM) formula is the following:
Rate of Return Rule of 72 Actual # of Years
2% 36.0
3% 24.0
5% 14.4
7% 10.3
9% 8.0
12% 6.0
25% 2.9
50% 1.4
72% 1.0
100% 0.7
Notice that it gives an estimate
How to Adjust the Rule of 72 for Higher Accuracy
The Rule of 72 is more accurate if it is adjusted to more closely resemble the compound interest formula—which effectively transforms the Rule of 72 into the Rule of 69.3. Many investors prefer to use the Rule of 69.3 rather than the Rule of 72. For maximum accuracy—particularly for continuous compounding interest rate instruments—use the Rule of 69.3.
The number 72 has many convenient factors including two, three, four, six, and nine. This convenience makes it easier to use the Rule of 72 for a close approximation of compounding periods.
How to Calculate the Rule of 72 Using Matlab
The calculation of the Rule of 72 in Matlab requires running a simple command of "years = 72/return," where the variable "return" is the rate of return on investment and "years" is the result for the Rule of 72. The Rule of 72 is also used to determine how long it takes for money to halve in value for a given rate of inflation. For example, if the rate of inflation is 4%, a command "years = 72/inflation" where the variable inflation is defined as "inflation = 4" gives 18 years.
A Guide to Investing Outside the Stock Market
Many financial experts agree: the 60-40 asset allocation model is outdated. With equity forecasts at historic lows, top portfolio managers are turning to alternative assets like fine art to potentially enhance returns. Fine art is a $1.7 trillion-dollar asset class that's outpaced the S&P 500 by more than 2x in the last 25 years. With Masterworks, it's easy for anyone to invest in art.
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Comment: Posted to help income investors, retiree's and other interested investors. R72 can be used in many different and more complex ways.
Live Long and Prosper....
BONDS / FIXED INCOME
The Rule of 72: What It Is and How to Use It in Investing
By CAROLINE BANTON
Updated August 17, 2021
Reviewed by ANDY SMITH
Fact checked by SUZANNE KVILHAUG
What Is the Rule of 72?
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 the Rule of 72 Works
For example, the Rule of 72 states that $1 invested at an annual fixed interest rate of 10% would take 7.2 years ((72/10) = 7.2) to grow to $2. In reality, a 10% investment will take 7.3 years to double ((1.107.3 = 2).
The Rule of 72 is reasonably accurate for low rates of return. The chart below compares the numbers given by the Rule of 72 and the actual number of years it takes an investment to double.
Rate of Return Rule of 72 Actual # of Years Difference (#) of Years
2% 36.0 35 1.0
3% 24.0 23.45 0.6
5% 14.4 14.21 0.2
7% 10.3 10.24 0.0
9% 8.0 8.04 0.0
12% 6.0 6.12 0.1
25% 2.9 3.11 0.2
50% 1.4 1.71 0.3
72% 1.0 1.28 0.3
100% 0.7 1 0.3
Notice that although it gives an estimate, the Rule of 72 is less precise as rates of return increase.
The time value of money (TVM) formula is the following:
Rate of Return Rule of 72 Actual # of Years
2% 36.0
3% 24.0
5% 14.4
7% 10.3
9% 8.0
12% 6.0
25% 2.9
50% 1.4
72% 1.0
100% 0.7
Notice that it gives an estimate
How to Adjust the Rule of 72 for Higher Accuracy
The Rule of 72 is more accurate if it is adjusted to more closely resemble the compound interest formula—which effectively transforms the Rule of 72 into the Rule of 69.3. Many investors prefer to use the Rule of 69.3 rather than the Rule of 72. For maximum accuracy—particularly for continuous compounding interest rate instruments—use the Rule of 69.3.
The number 72 has many convenient factors including two, three, four, six, and nine. This convenience makes it easier to use the Rule of 72 for a close approximation of compounding periods.
How to Calculate the Rule of 72 Using Matlab
The calculation of the Rule of 72 in Matlab requires running a simple command of "years = 72/return," where the variable "return" is the rate of return on investment and "years" is the result for the Rule of 72. The Rule of 72 is also used to determine how long it takes for money to halve in value for a given rate of inflation. For example, if the rate of inflation is 4%, a command "years = 72/inflation" where the variable inflation is defined as "inflation = 4" gives 18 years.
A Guide to Investing Outside the Stock Market
Many financial experts agree: the 60-40 asset allocation model is outdated. With equity forecasts at historic lows, top portfolio managers are turning to alternative assets like fine art to potentially enhance returns. Fine art is a $1.7 trillion-dollar asset class that's outpaced the S&P 500 by more than 2x in the last 25 years. With Masterworks, it's easy for anyone to invest in art.
----------
Comment: Posted to help income investors, retiree's and other interested investors. R72 can be used in many different and more complex ways.
Live Long and Prosper....