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Compounding Rules of 72, 115 and 144

September 6, 2012

Compounding occurs when interest is paid on reinvested interest while continuing to be paid on the original principal. Compounding uses time as an ally – the longer the process, the greater the growth.

 

Interest can be compounded daily, monthly, annually or any other way that a lender and borrower agree.  Effective annual yield quotes take compounding into account over the investment period or term.

 

Following is an example of 7% interest compounded once a year for three years.

 

Principal                                                                                $100,000

Interest year 1                                                                            7,000

New principal balance                                                        $107,000

Interest year 2                                                                            7,490

New principal balance                                                        $114,490

Interest year 3                                                                            8,014

New principal balance                                                        $122,504

Effective annual yield                                                               7.5%

 

The rules of 72 and 115 provide a quick way of seeing the value and speed of compounding.  These are short cuts to determine how long it takes compounded money to double and triple.  To calculate how long it takes money to double, divide the interest rate into 72.  To see how long money triples, divide it into 115.  Assuming a 7% interest rate, it will take approximately 10.3 years for the original principal to double and 16.4 years to triple.

 

There is also a rule of 144.  This gives an approximation of how long it takes a series of equal annual payments to double.  For example, $1,000 a year deposited at 7% for 20.6 years will have $20,600 double to become $41,200.

 

 

 

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

11.00%

12.00%

Rule of 72 # yrs. to double

18.0

14.4

12.0

10.3

9.0

8.0

7.2

6.5

6

Rule of 115 # yrs. to triple

28.8

23.0

19.2

16.4

14.4

12.8

11.5

10.5

9.6

Rule of 144 # yrs. a series of pmts. double 

36.0

28.8

24.0

20.6

18.0

16.0

14.4

13.1

12.0

 

Compounding fallacy: The rules of 72, 115 and 144 assume that the interest will be reinvested and compounded at the original rate.  This is the case when you invest in a CD with the interest accumulating or a zero coupon or discounted bond.  However, when you invest in a CD, bond or stock that is paying the interest or dividend annually, that payment would have to be reinvested at the original rate in order to reach the targeted goal as planned.  This is unlikely for a number of reasons, one of which is that short term rates are usually lower than long term rates.  When you originally invested, you received a rate for a term that is longer than the remaining term will be for the interest payments.  Unless market rates have increased, or you found a different way to invest with greater returns, you are not likely to  get the same rate as the original rate of the investment.  Further, taxes can be a factor in diminishing the amount that you can reinvest.  However, using these rules will give you a way of estimating the final amounts and a basis of comparing one investment to another.

5 Comments leave one →
  1. Rick permalink
    September 6, 2012 4:24 pm

    What’s Zero into 72?

  2. September 6, 2012 6:51 pm

    Another friend emailed me the following:
    Ahhh, the eternal optimist.
    In my opinion, your table should start at 0.5% interest and increase in 0.5% increments; you can forget about the 8+% rates, at least for the foreseeable future.

  3. Jim Edge permalink
    September 7, 2012 12:30 pm

    Thanks; I enjoy shortcuts like these.

    James B. Edge, Jr., MBA, CPA-ABV

    Cornerstone Financial Management, Inc.

    P. O. Box 17242 Richmond, VA 23226

    804-320-3499 (office) 804-283-1588 (cell)

    jedge@cfm-valuation.com

    Focused on professional client valuations

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  5. September 4, 2015 2:48 pm

    The rule of 72 is indeed a moving target. It’s importance is to impress upon clients the importance of compounding for the long term.

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