How long will it take to DOUBLE your money at a given rate of return?
How long will it take inflation to HALVE the purchasing power of your savings or present salary?
Are your investments REALLY profitable, considering inflation?

The Rule of 72 is called that because at 10%, money will double every 7.2 years.  The "Rule of 72" gives you quick approximate answers to those questions above.  As the Rule of 72 is a "rule of thumb", it does not give exact results, but its approximations are close enough to give you an idea of what's happening.
(If you want exact numbers, see the calculations and examples near the end of this page.)

If your interest rate or rate of return is 10%, according to the Rule of 72 it will take about 7.2 years to double an initial amount.

The general rule is to divide 72 by the rate of return, and the Rule of 72 will give you the approximate number of years required to double the starting amount.

             Years Required
     Rate %    to Double
     ------  --------------
         5%      14.4
       7.5%       9.6
        10%       7.2
        15%       4.8
  

Here are a few examples of how much the Rule of 72 says you would have at the end of a specified number of years, starting with $5000, for different rates of return.

     Rate %            5%      7.5%       10%       15%
     1st Double  14.4 yrs   9.6 yrs   7.2 yrs   4.8 yrs
     ----------  --------  --------  --------  --------
     Years
     (start)        5,000     5,000     5,000     5,000
     ----------  --------  --------  --------  --------
      4.8 years                                  10,000
      7.2 years                        10,000
      9.6 years              10,000              20,000
     14.4 years    10,000              20,000    40,000
     19.2 years              20,000              80,000
     21.6 years                        40,000
     24.0 years                                 160,000
     28.8 years    20,000    40,000    80,000   320,000
  

Keep in mind that the dollars (or other fiat currency savings or salary) you may have in 28.8 years will almost certainly purchase significantly less than the same number of fiat dollars will purchase today.  Just as the fiat dollars you may have had 28.8 years ago (1976) won't get you much today (2005).
(See below for a discussion of the Rule of 72 and Inflation.)

The Rule of 72 also allows you to calculate what rate of interest or return you would need to double your money in a specified time.

The rule in this case is to divide 72 by number of years you would like it to take, and the Rule of 72 will give you an approximation to the rate of return required to double the starting amount.

     Years Required   Return %
       to Double     Necessary
     --------------  ---------
          2            36.0%
          5            14.4%
          7.2          10.0%
         10             7.2%
  

Your government (regardless of which one, including that of the "good old U.S. of A.") deliberately and knowingly LIES to you on a regular and calculated basis.  Your government DOES NOT deserve your support in any manner.  Your government is run by and for a cabal of crooks who make the mafia and past tyrants appear as petty amateurs.  Official talk of democracy and their various programs are merely for propagandizing and pacifying you.

What does this have to do with the Rule of 72 and inflation?  Because most people are totally ignorant of the machinations of governments and their Central Banks (in the U.S., the Federal Reserve) in general, and the money and credit systems in particular, you need to read the following.
("Machination" loosely defined: "Screwing you over".)

There is no "sound" money (reality related) in general use ANYWHERE on this planet.  All present day money (and credit) systems are fiat based.
("Fiat" defined re money and credit: "Decree".)

These fiat systems are controlled by the Central Banks.  To the extent that fiat money and credit that we are subject to have any value, it is only because governments decree that their monetary systems are the official ones.

Fiat money and credit do not represent anything real.  Fiat money and credit is only numbers and computer storage bits that can be arbitrarily changed at any time.  The fiat systems are set up entirely for the benefit of the banking system (particularly the owners of the Central Banks), and for the advantage of politicians, bureaucrats, and various clients and patrons of government.   They are NOT for the benefit of most wage and salary earners, businessmen, tradesmen, manufacturers, importers, exporters, retirees...

Under a fiat money system, the amount of money and credit is continually increased.  (At least until the system implodes as ALL previous ones eventually have.)  Those first in line at the trough get the benefit.  By the time it gets to most people, perhaps you, it's too late to do you any good -- you've already been paying higher prices with money earned at the old rate.

This increasing supply of money and credit is itself INFLATION.  The popular (captive) press, in the interests of the bankers and government completely ignore inflation.  That is, while they use the word "inflation" incessantly, they never discuss inflation.  What they discuss is the RESULTS of inflation, which is the constantly increasing COST OF LIVING (COL) as represented by the fraudulently calculated CONSUMER PRICE INDEX (CPI).

The Consumer Price Index (CPI) is purportedly a measure of the Cost of Living (COL), but the calculations deliberately understate real cost increases, and completely ignore increases in government taxes and "fees" and the increasing costs of increasing government regulations.

BOTTOM LINE -- Your government LIES to you about the Consumer Price Index (CPI) and the Cost of Living (COL).

Anyway, your government grossly understates the RESULT of inflation, which is an increasing Cost of Living (COL) for you. This dramatically, drastically, affects the purchasing power of any savings or investments you may have, and ALSO negatively affects the REAL RATE OF RETURN on your investments and speculations.

The Rule of 72 also applies to purchasing power halving calculations.

If the Cost of Living (COL) rate increase is 10%, according to the Rule of 72 it will take about 7.2 years to lose half the purchasing power of an initial amount.

At an official government Consumer Price Index (CPI) increase rate of 3.5%, the purchasing power of any savings will be halved in about 20 years.  Maybe you figure you can live with that.  But remember, THE GOVERNMENT LIES ABOUT THE CPI and, thus, the actual Cost of Living (COL) rate of increase.  A "Truth in Government (TIGF)" adjustment has to be added to the Consumer Price Index (CPI) to get a better estimate of the Cost of Living (COL).  It is substantial.  So, at a more realistically estimated Cost of Living (COL) increase rate of 12%, the purchasing power of any savings will be halved in just six years.

Again, the general rule is to divide 72 by the Cost of Living (COL) rate of increase, and the Rule of 72 will give you the approximate number of years required to halve the purchasing power of the starting amount.

Are you really profiting with your investments? In REAL terms?

Say you bought $1000 of stock 10 years ago.  Say that now you could sell it for $2000.  You might think (and the IRS would insist) that you have a profit of $1000.  But what if the real rate of the increase in the Cost of Living (COL) was such that while the $1000 ten years ago would buy you 10 widgets, the $2000 today would buy you only 9 widgets (of the same quality and usefulness).  You would actually suffer a LOSS in buying power (a real capital loss) of about 10%.  You would not have a profit (a "capital gain") of 100% -- in REAL terms.

I used an estimated "fudge factor" -- I called it a "Truth-in-Government Adjustment" -- to modify the results to what I thought more realistic.

Remember the Rule of 72.  If the Cost of Living (COL) is increasing at a rate of 6% per year, see what happens:  72/6 = 12.  That means that the VALUE (purchasing power) of a lump sum will be HALVED in 12 years.  Similarly, if you can gain 6% per year on an investment, it will double in 12 years, in nominal dollars.  Of course, if the Cost of Living (COL) rate is also at 6% per year, that means you will have spun your wheels for NOTHING (for no increase in purchasing power) for 12 years.  And, of course, the IRS will want its "share" of that so-called gain, not allowing "indexing" for inflation.  Essentially, the IRS IS TAXING YOUR CAPITAL.  Which explains why this country is going into the dumpster (or may already have arrived there by the time you read this).  Anyway, that means you have to do substantially better than inflation -- or arrange your affairs to keep the thievin' hands of the IRS out of your pocket.

Like any rule of thumb, the Rule of 72 is only good for approximations. For exact calculations, here is a derivation with an example:

     Principal            P
     Interest rate (%)    r
     Number of years      t
     Desired doubling     2P

     The compounding equation is (for doubling):

       2P = P * (1 + r/100)^t

     Note that the symbol "^" denotes exponentiation (e.g., 2^3 = 8).

     For the interest or return rate of r = 10%, the equation becomes:

       2P = P * (1 + 10/100)^t

     Canceling the "P"s and rearranging:

       2 = (1 + 10/100)^t
       2 = 1.1^t

     From calculus we know that natural logarithms ("ln") have the following property:

       ln (a^b) = b * ln (a)

     Continuing with our derivation (including taking the log of both sides):

       ln (2) = ln (1.1^t)
       ln (2) = t * ln (1.1)

       t = ln (2) / ln (1.1)

     Using your trusty calculator with the "ln" key, you get:

       t = 7.2725 years

     which is close to the Rule of 72 approximation of 7.2 years (at 10%).
  

You can solve the equation for other rates (r) to see how close the Rule of 72 results comes to the actual results.  Here's a table showing the actual number of years required to double the principal based on various rates (r), along with the number of years that the Rule of 72 estimates.

                   Years to Double
                Actual      Rule of 72   Approximation
     Rate %  Calculation  Approximation     Error%
     ------  -----------  -------------  -------------
        1       69.66         72.00         + 3.4%
        2       35.00         36.00         + 2.9%
        3       23.45         24.00         + 2.3%
        4       17.67         18.00         + 1.9%
        5       14.21         14.40         + 1.3%
        6       11.90         12.00         + 0.8%
        7       10.24         10.29         + 0.5%
        8        9.01          9.00         - 0.1%
        9        8.04          8.00         - 0.5%
       10        7.27          7.20         - 1.0%
       15        4.96          4.80         - 3.2%
       20        3.80          3.60         - 5.3%
       25        3.11          2.88         - 7.4%
       30        2.64          2.40         - 9.1%
       40        2.06          1.80         -12.6%
       50        1.71          1.44         -15.8%
       75        1.24          0.96         -22.6%
      100        1.00          0.72         -28.0%
  

Please bookmark this page before you visit the next site.
David A. Bean's Wealth Main Page     CPT Main Page