The previous thread mentioned about how the compounding effect makes Warren Buffet being one of the richest man in the world. It is attributable to his ability to achieve a sustainable annual compounded rate of return (“ACRR”) at 26% for 41 years.
If Warren Buffet was only able to achieve a normal ACRR of 10% instead of 26%, what would be his performance after 41 years? Some might think that since 10 is about 38% of 26, so his performance will be around 38% of what he could achieve base on the ACRR of 26% after 41 years, i.e.USD57,000 (= 38% * USD150,000).
Those who are familiar to mathematic would argue that an investment with an ACRR of 10% does not worth USD57,000 after 41 years. Indeed, the investment merely appreciate to USD597 (=USD12 * [1+0.1]^41). The Table below shows more precisely how the gap in between 2 investments with different rate of return becomes wider after incorporating time period:-
From the table above, we should notice that the Investment A has a smaller return than the Investment B. Hence, the value of Investment A is far from equals to the value of Investment B after 11 years. The value of Investment A only equals to 22% of the value of Investment B (Another way to describe is to use the reciprocal of the percentage that indicates the value of Investment B is 4.45 times [=1/0.22] of the value of Investment A after 11 years).
The time effect will further amplify the gap in between the value of Investment A and of Investment B. The value of Investment A is then only 0.38% of the value of Investment B after 41 years (the reciprocal of the percentage indicates the value of Investment B is 261.87 times [=1/0.0038] of the value of Investment A after 41 years)!!!
Thus we should understand that the compounding effect is based on geometric growth rather than arithmetic growth. As an arithmetic growth is a function where one unit of principal makes exactly one unit of growth, whereby a geometric growth is one where adding one unit of principal makes more than one unit of growth. Put it another way to describe that the geometric growth is growing not only the principal but also the incremental interest earned by the principal.
Of course, we should take note that the compounding effect is a double edge sword which could bring positive or negative effect to us. If we were getting into an unproductive debt such as personal loan, consumer loan or credit card loan, the compounding effect will be against us (as there are some credit loans will charge us up to 18% interest per year to the due amount, and it is not even to take into the extreme case of the loan-shark rate). So we need make sure the compounding effect to be our friend by engaging activities that can stimulate positive compounding return.
Now it comes to an overall summary of the compounding effect that the larger the ACRR and the longer time tenure we could sustain the ACRR, the greater impact of compounding effect. And in order to enjoy the power of compounding effect, we should remember the golden rule of accumulation, that is start to invest as earlier as possible.
[Note 1: Formulas of measuring compounding interest
Single compounding period per year function:
FV = PV ( 1+r )^t
Multi compounding period per year function:
FV = PV * (1 + r/n)^(n* t)
Continuous compounding period per year (Exponential) function:
FV = PV * e^(r * t)
* FV = Future Value
* PV = Present Value
* t = Total time in years
* n = Number of compounding periods per year
* r = Nominal annual interest rate expressed as a decimal]
[Note 2: A typical story about the compounding effect
If the Native American tribe (the Red Indian) that accepted goods worth 60 guilders for the sale of Manhattan in 1626 had invested the money in a Dutch bank at 6.5% interest, compounded annually, then in 2009 their investment would be worth over €900 billion (around USD1.3 trillion), more than the assessed value of the real estate in all five boroughs of New York City. With a 6.0% interest however, the value of their investment today would have been €130 billion (1/7th as much!).]
If Warren Buffet was only able to achieve a normal ACRR of 10% instead of 26%, what would be his performance after 41 years? Some might think that since 10 is about 38% of 26, so his performance will be around 38% of what he could achieve base on the ACRR of 26% after 41 years, i.e.USD57,000 (= 38% * USD150,000).
Those who are familiar to mathematic would argue that an investment with an ACRR of 10% does not worth USD57,000 after 41 years. Indeed, the investment merely appreciate to USD597 (=USD12 * [1+0.1]^41). The Table below shows more precisely how the gap in between 2 investments with different rate of return becomes wider after incorporating time period:-
From the table above, we should notice that the Investment A has a smaller return than the Investment B. Hence, the value of Investment A is far from equals to the value of Investment B after 11 years. The value of Investment A only equals to 22% of the value of Investment B (Another way to describe is to use the reciprocal of the percentage that indicates the value of Investment B is 4.45 times [=1/0.22] of the value of Investment A after 11 years).
The time effect will further amplify the gap in between the value of Investment A and of Investment B. The value of Investment A is then only 0.38% of the value of Investment B after 41 years (the reciprocal of the percentage indicates the value of Investment B is 261.87 times [=1/0.0038] of the value of Investment A after 41 years)!!!
Thus we should understand that the compounding effect is based on geometric growth rather than arithmetic growth. As an arithmetic growth is a function where one unit of principal makes exactly one unit of growth, whereby a geometric growth is one where adding one unit of principal makes more than one unit of growth. Put it another way to describe that the geometric growth is growing not only the principal but also the incremental interest earned by the principal.
Of course, we should take note that the compounding effect is a double edge sword which could bring positive or negative effect to us. If we were getting into an unproductive debt such as personal loan, consumer loan or credit card loan, the compounding effect will be against us (as there are some credit loans will charge us up to 18% interest per year to the due amount, and it is not even to take into the extreme case of the loan-shark rate). So we need make sure the compounding effect to be our friend by engaging activities that can stimulate positive compounding return.
Now it comes to an overall summary of the compounding effect that the larger the ACRR and the longer time tenure we could sustain the ACRR, the greater impact of compounding effect. And in order to enjoy the power of compounding effect, we should remember the golden rule of accumulation, that is start to invest as earlier as possible.
[Note 1: Formulas of measuring compounding interest
Single compounding period per year function:
FV = PV ( 1+r )^t
Multi compounding period per year function:
FV = PV * (1 + r/n)^(n* t)
Continuous compounding period per year (Exponential) function:
FV = PV * e^(r * t)
* FV = Future Value
* PV = Present Value
* t = Total time in years
* n = Number of compounding periods per year
* r = Nominal annual interest rate expressed as a decimal]
[Note 2: A typical story about the compounding effect
If the Native American tribe (the Red Indian) that accepted goods worth 60 guilders for the sale of Manhattan in 1626 had invested the money in a Dutch bank at 6.5% interest, compounded annually, then in 2009 their investment would be worth over €900 billion (around USD1.3 trillion), more than the assessed value of the real estate in all five boroughs of New York City. With a 6.0% interest however, the value of their investment today would have been €130 billion (1/7th as much!).]
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