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The additional growth or additional interest, resulting from the compounding effects of - for example - interest on interest.
1. ''Financial maths.''


Another example is the compounding effect of growth on growth.  
In maths, compounding effects are the additional growth or additional interest, resulting from the compounding effects of - for example - interest on interest.




For example, interest quoted at 6% per annum, compounded annually, for two years maturity, means that the interest accumulated after two years is:
<span style="color:#4B0082">'''Example 1: Compounding for two years at 5% per annum'''</span>


= [1.06 x 1.06] - 1
Interest quoted at 5% per annum, compounded annually, for two years maturity, means that the interest accumulated after two years is:


= 12.36% for the two year period.
= (1.05 x 1.05) - 1
 
= 10.25% for the two year period.




Without the additional interest on interest, the total interest would have been simply  
Without the additional interest on interest, the total interest would have been simply  


6% per annum x 2 years  
5% per annum x 2 years  


= 12.00%.
= 10.00%.




So the compounding effect of interest on interest here  
So the compounding effect of interest on interest here  


= 12.36% - 12.00%  
= 10.25% - 10.00%  


= 0.36% over the two year period (= 6% x 6%).
= 0.25% over the two year period (= 5% x 5%).




When both the number of periods and the rate of growth/interest are low, compounding effects are relatively small.
When both the number of periods and the rate of growth/interest are low, compounding effects are relatively small.
When either the number of periods or the rate of growth/interest - or both - are greater, compounding effects become very much larger.
 
When either the number of periods or the rate of growth/interest - or both - are greater, compounding effects quickly become very much larger.
 
 
 
<span style="color:#4B0082">'''Example 2: Compounding for two years at 50% per annum'''</span>
 
Sales are growing at 50% per annum, for two years.
 
This means that the total growth after two years is:
 
= (1.50 x 1.50) - 1
 
= 125% for the two year period.
 
 
Without the additional growth on growth, the total growth would have been simply
 
50% per annum x 2 years
 
= 100%.
 
 
So the compounding effect of growth on growth here
 
= 125% - 100%
 
= 25% over the two year period (= 50% x 50%).
 
 
 
<span style="color:#4B0082">'''Example 3: Compounding for 20 years at 5% per annum'''</span>
 
Interest quoted at 5% per annum, compounded annually, for 20 years maturity, means that the interest accumulated after 20 years is:
 
= 1.05<sup>20</sup> - 1
 
= 165% for the 20-year period.
 
 
Without the additional interest on interest, the total interest would have been simply
 
5% per annum x 20 years
 
= 100%.
 
 
So the compounding effect of interest on interest here
 
= 165% - 100%
 
= 65% over the 20-year period.
 
 
[[File:Compounding effects illustration.png|{850}px|850px]]
 
 
2.  ''Risk management.''
 
Additional adverse consequences which occur when multiple adverse conditions arise at the same time.
 
 
:<span style="color:#4B0082">'''''Related global risks with compounding effects'''''</span>
 
:"[Global] risks can also interact with each other to form a 'polycrisis' – a cluster of related global risks with compounding effects, such that the overall impact exceeds the sum of each part."
 
:''World Economic Forum (WEF) - Global Risks Report 2023 - p57.''




== See also ==
== See also ==
* [[Adverse]]
* [[Compound]]
* [[Compound interest]]
* [[Compound interest]]
* [[Compounding factor]]
* [[Compounding factor]]
* [[Consequential risk]]
* [[Continuously compounded rate of return]]
* [[Continuously compounded rate of return]]
* [[Exponential growth]]
* [[Geometric progression]]
* [[Global risk]]
* [[Linear]]
* [[Polycrisis]]
* [[Risk management]]
* [[Simple interest]]
* [[World Economic Forum]]  (WEF)


[[Category:Manage_risks]]
[[Category:Manage_risks]]

Latest revision as of 21:59, 18 April 2023

1. Financial maths.

In maths, compounding effects are the additional growth or additional interest, resulting from the compounding effects of - for example - interest on interest.


Example 1: Compounding for two years at 5% per annum

Interest quoted at 5% per annum, compounded annually, for two years maturity, means that the interest accumulated after two years is:

= (1.05 x 1.05) - 1

= 10.25% for the two year period.


Without the additional interest on interest, the total interest would have been simply

5% per annum x 2 years

= 10.00%.


So the compounding effect of interest on interest here

= 10.25% - 10.00%

= 0.25% over the two year period (= 5% x 5%).


When both the number of periods and the rate of growth/interest are low, compounding effects are relatively small.

When either the number of periods or the rate of growth/interest - or both - are greater, compounding effects quickly become very much larger.


Example 2: Compounding for two years at 50% per annum

Sales are growing at 50% per annum, for two years.

This means that the total growth after two years is:

= (1.50 x 1.50) - 1

= 125% for the two year period.


Without the additional growth on growth, the total growth would have been simply

50% per annum x 2 years

= 100%.


So the compounding effect of growth on growth here

= 125% - 100%

= 25% over the two year period (= 50% x 50%).


Example 3: Compounding for 20 years at 5% per annum

Interest quoted at 5% per annum, compounded annually, for 20 years maturity, means that the interest accumulated after 20 years is:

= 1.0520 - 1

= 165% for the 20-year period.


Without the additional interest on interest, the total interest would have been simply

5% per annum x 20 years

= 100%.


So the compounding effect of interest on interest here

= 165% - 100%

= 65% over the 20-year period.


{850}px


2. Risk management.

Additional adverse consequences which occur when multiple adverse conditions arise at the same time.


Related global risks with compounding effects
"[Global] risks can also interact with each other to form a 'polycrisis' – a cluster of related global risks with compounding effects, such that the overall impact exceeds the sum of each part."
World Economic Forum (WEF) - Global Risks Report 2023 - p57.


See also