Compounding effect
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.
