Compounding effect: Difference between revisions
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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''' | <span style="color:#4B0082">'''Example 1: Compounding for two years at 5% per annum'''</span> | ||
Interest quoted at | Interest quoted at 5% per annum, compounded annually, for two years maturity, means that the interest accumulated after two years is: | ||
= ( 1. | = (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 | ||
5% per annum x 2 years | |||
= | = 10.00%. | ||
So the compounding effect of interest on interest here | So the compounding effect of interest on interest here | ||
= | = 10.25% - 10.00% | ||
= 0. | = 0.25% over the two year period (= 5% x 5%). | ||
| Line 30: | Line 30: | ||
When either the number of periods or the rate of growth/interest - or both - are greater, compounding effects quickly 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.
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.
