Compounding effect: Difference between revisions

From ACT Wiki
Jump to navigationJump to search
imported>Doug Williamson
(Add link.)
imported>Doug Williamson
(Layout.)
Line 1: Line 1:
The additional growth or additional interest, resulting from the compounding effects of - for example - interest on interest.
The additional growth or additional interest, resulting from the compounding effects of - for example - interest on interest.


Another example is the compounding effect of growth on growth.


 
<span style="color:#4B0082">'''Example 1: Compounding for two years at 6% per annum'''</span>
'''Example'''  


Interest quoted at 6% per annum, compounded annually, for two years maturity, means that the interest accumulated after two years is:
Interest quoted at 6% per annum, compounded annually, for two years maturity, means that the interest accumulated after two years is:
Line 30: Line 28:


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 60% per annum'''</span>
Sales are growing at 60% per annum, for two years.
This means that the total growth after two years is:
= (1.60 x 1.60) - 1
= 156% for the two year period.
Without the additional growth on growth, the total growth would have been simply
60% per annum x 2 years
= 120%.
So the compounding effect of growth on growth here
= 156% - 120%
= 36% over the two year period (= 60% x 60%).
<span style="color:#4B0082">'''Example 3: Compounding for 20 years at 6% per annum'''</span>
Interest quoted at 6% per annum, compounded annually, for 20 years maturity, means that the interest accumulated after 20 years is:
= 1.06<sup>20</sup> - 1
= 221% for the 20-year period.
Without the additional interest on interest, the total interest would have been simply
6% per annum x 20 years
= 120%.
So the compounding effect of interest on interest here
= 221% - 120%
= 101% over the 20-year period.





Revision as of 15:11, 26 December 2020

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


Example 1: Compounding for two years at 6% per annum

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

= 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%.


So the compounding effect of interest on interest here

= 12.36% - 12.00%

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


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 60% per annum

Sales are growing at 60% per annum, for two years.

This means that the total growth after two years is:

= (1.60 x 1.60) - 1

= 156% for the two year period.


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

60% per annum x 2 years

= 120%.


So the compounding effect of growth on growth here

= 156% - 120%

= 36% over the two year period (= 60% x 60%).


Example 3: Compounding for 20 years at 6% per annum

Interest quoted at 6% per annum, compounded annually, for 20 years maturity, means that the interest accumulated after 20 years is:

= 1.0620 - 1

= 221% for the 20-year period.


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

6% per annum x 20 years

= 120%.


So the compounding effect of interest on interest here

= 221% - 120%

= 101% over the 20-year period.


See also