Compounding effect: Difference between revisions

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The additional growth or additional interest, resulting from the compounding effects of - for example - interest on interest.
1. ''Financial maths.''
For example, interest quoted at 6% per annum, compounded annually, for two years maturity, means that the interest accumulated after two years is:


= [1.06 x 1.06] - 1
In maths, compounding effects are the additional growth or additional interest, resulting from the compounding effects of - for example - interest on interest.


= 12.36% for the two year period.


Without the additional interest on interest, the total interest would have been simply 6% per annum x 2 years = 12.00%.
<span style="color:#4B0082">'''Example 1: Compounding for two years at 5% per annum'''</span>
So the compounding effect of interest on interest here = 12.36% - 12.00% = 0.36% over the two year period (= 6% x 6%).
 
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 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:Interest_Rate_Risk]]
[[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