De-compound
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.
It is sometimes written as decompound.
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%
