Compounding effect: Difference between revisions
imported>Doug Williamson (Layout.) |
imported>Doug Williamson (Add illustration.) |
||
| Line 1: | Line 1: | ||
Compounding effects are the additional growth or additional interest, resulting from the compounding effects of - for example - interest on interest. | |||
<span style="color:#4B0082">'''Example 1: Compounding for two years at | <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 31: | Line 31: | ||
<span style="color:#4B0082">'''Example 2: Compounding for two years at | <span style="color:#4B0082">'''Example 2: Compounding for two years at 50% per annum'''</span> | ||
Sales are growing at | Sales are growing at 50% per annum, for two years. | ||
This means that the total growth after two years is: | This means that the total growth after two years is: | ||
= (1. | = (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 | 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 | 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 | <span style="color:#4B0082">'''Example 3: Compounding for 20 years at 5% per annum'''</span> | ||
Interest quoted at | Interest quoted at 5% per annum, compounded annually, for 20 years maturity, means that the interest accumulated after 20 years is: | ||
= 1. | = 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 | 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 | So the compounding effect of interest on interest here | ||
= | = 165% - 100% | ||
= | = 65% over the 20-year period. | ||
[[File:Compounding effects illustration.png]] | |||
| Line 85: | Line 89: | ||
* [[Compounding factor]] | * [[Compounding factor]] | ||
* [[Continuously compounded rate of return]] | * [[Continuously compounded rate of return]] | ||
* [[ | * [[Exponential growth]] | ||
* [[Geometric]] | |||
* [[Linear]] | |||
[[Category:Manage_risks]] | [[Category:Manage_risks]] | ||
Revision as of 00:12, 29 December 2020
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.
File:Compounding effects illustration.png
