# De-compound

Jump to: navigation, search

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%