Compounding effect
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.
