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. | 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 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: | ||
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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.
