https://wiki-dev.treasurers.org/w/index.php?action=history&feed=atom&title=De-compoundDe-compound - Revision history2026-04-27T01:44:51ZRevision history for this page on the wikiMediaWiki 1.40.0https://wiki-dev.treasurers.org/w/index.php?title=De-compound&diff=13817&oldid=previmported>Doug Williamson: Create page. Sources: linked pages.2021-03-27T15:54:34Z<p>Create page. Sources: linked pages.</p>
<p><b>New page</b></p><div>''Compounding.''<br />
<br />
To compound means:<br />
* to calculate interest, return or growth on an accumulating total, <br />
* including earlier amounts of interest, return or growth.<br />
<br />
<br />
De-compounding is the reverse process.<br />
<br />
It calculates a compound rate per period for a shorter period of time, based on a total rate of growth for a longer period.<br />
<br />
<br />
<span style="color:#4B0082">'''Example: de-compounding calculation'''</span><br />
<br />
Total growth for a two-year period = 69%. <br />
<br />
What is the average compound rate of growth per year, for the two years?<br />
<br />
<br />
Rate per year = (End amount / Starting amount)<sup>(1/n)</sup> - 1<br />
<br />
''Where:''<br />
<br />
n = number of years<br />
<br />
<br />
Let's say the starting amount = $100m<br />
<br />
Total growth for two years = $100m x 0.69<br />
<br />
= $69m<br />
<br />
<br />
End amount = $100m + $69m<br />
<br />
= $169m<br />
<br />
<br />
The rate per year is: <br />
<br />
= (169 / 100)<sup>(1/2)</sup> - 1 <br />
<br />
= 1.69<sup>(1/2)</sup> - 1 <br />
<br />
= '''30%'''<br />
<br />
<br />
Check:<br />
<br />
Growth for the first year:<br />
<br />
= $100m x 0.30<br />
<br />
= $30m<br />
<br />
<br />
Balance at the end of the first year:<br />
<br />
$100m + $30m<br />
<br />
= $130m<br />
<br />
<br />
Growth for the second year:<br />
<br />
= $130m x 0.30<br />
<br />
= $39m<br />
<br />
<br />
Balance at the end of the second year:<br />
<br />
$130m + $39m<br />
<br />
= $169m<br />
<br />
<br />
Total percentage growth for the two-year period:<br />
<br />
169/100 - 1<br />
<br />
= 1.69 - 1<br />
<br />
= 0.69<br />
<br />
= '''69%'''<br />
<br />
<br />
== See also ==<br />
* [[Compound]]<br />
* [[Compound Annual Growth Rate]]<br />
* [[Compounding effect]]<br />
* [[Compound interest]]<br />
* [[Effective annual rate]]<br />
* [[Interest]]<br />
* [[Interest rate]]<br />
* [[Nominal annual rate]]<br />
* [[Simple interest]]<br />
<br />
[[Category:The_business_context]]<br />
[[Category:Corporate_finance]]<br />
[[Category:Investment]]<br />
[[Category:Long_term_funding]]<br />
[[Category:Financial_products_and_markets]]</div>imported>Doug Williamson