De-compound

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Compounding.

To compound means:

  • to calculate interest, return or growth on an accumulating total,
  • including earlier amounts of interest, return or growth.


De-compounding is the reverse process.

It calculates a compound rate per period for a shorter period of time, based on a total rate of growth for a longer period.


Example: de-compounding calculation

Total growth for a two-year period = 69%.

What is the average compound rate of growth per year, for the two years?


Rate per year = (End amount / Starting amount)(1/n) - 1

Where:

n = number of years


Let's say the starting amount = $100m

Total growth for two years = $100m x 0.69

= $69m


End amount = $100m + $69m

= $169m


The rate per year is:

= (169 / 100)(1/2) - 1

= 1.69(1/2) - 1

= 30%


Check:

Growth for the first year:

= $100m x 0.30

= $30m


Balance at the end of the first year:

$100m + $30m

= $130m


Growth for the second year:

= $130m x 0.30

= $39m


Balance at the end of the second year:

$130m + $39m

= $169m


Total percentage growth for the two-year period:

169/100 - 1

= 1.69 - 1

= 0.69

= 69%


See also