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Subject: [OASIS Issue Tracker] Updated: (OFFICE-3040) 6.12.36: PDurationformula appears incorrect

• From: OASIS Issues Tracker <workgroup_mailer@lists.oasis-open.org>
• To: office@lists.oasis-open.org
• Date: Tue, 28 Sep 2010 12:08:24 -0400 (EDT)

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[ http://tools.oasis-open.org/issues/browse/OFFICE-3040?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]

Eike Rathke updated OFFICE-3040:
--------------------------------

Component/s: OpenFormula
Part 2 (Formulas)

> 6.12.36: PDuration formula appears incorrect
> --------------------------------------------
>
>                 Key: OFFICE-3040
>                 URL: http://tools.oasis-open.org/issues/browse/OFFICE-3040
>             Project: OASIS Open Document Format for Office Applications (OpenDocument) TC
>          Issue Type: Bug
>          Components: OpenFormula, Part 2 (Formulas), Public Review
>    Affects Versions: ODF 1.2 CD 05
>            Reporter: Eric Patterson
>            Assignee: Robert Weir
>             Fix For: ODF 1.2 CD 06
>
>
> I believe that the denominator in the Pduration formula should be log(1+rate), not log(rate)
> Actual:
> PDURATION=(log⁡(desiredValue)-log⁡(currentValue))/log⁡(rate)
> Expected:
> PDURATION=(log⁡(desiredValue)-log⁡(currentValue))/log⁡(1+rate)
> From wolfram the formula for interest calculations is
> FV = PV(1 + r/f)^(nf)
> where
> FV = future value
> PV = present value
> r = interest rate
> f = compounding frequency
> n = number of periods
> Given that pduration makes no mention of any compounding frequency it should be assumed to be 1.  so the formula becomes
> FV = PV(1 + r)^n
> In the case of PDURATION we want to solve for n given FV, PV, and r
> FV / PV = (1 + r)^n
> n = log_(1+r)(FV/PV) where log_(1+r) is log base 1+ r
> through change of base formula
> n = log_(1+r)(FV/PV) = log(FV/PV) / log(1+r) = (log(FV) - log(PV))/log(1+r) where the base of log is irrelevant so long as it is consistent.
> Below is a less rigorous justification for the (1+r) in the original equation:
> The (1+r) is originally present in the compound interest formula as r is simply the rate of interest, not the growth factor.  An investment that grows as 6% would have r = 0.06.  Over 1 term r*PV evaluates to only the growth of the investment.  We must add to the growth the value of the original investment.  so FV = PV + r*PV = PV*(1+r).  Hence the original growth factor in the formula must be (1+r) and the derivation from that to the PDURATION formula has already been shown.

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