# Compounding effect

1. Financial maths.

In maths, 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.

2. Risk management.