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Subject: [OASIS Issue Tracker] Created: (OFFICE-3040) Needs-Discussion:6.12.36: PDuration formula appears incorrect

• From: OASIS Issues Tracker <workgroup_mailer@lists.oasis-open.org>
• To: office@lists.oasis-open.org
• Date: Mon, 26 Jul 2010 19:55:13 -0400 (EDT)

```Needs-Discussion: 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
Affects Versions: ODF 1.2 CD 05
Reporter: Eric Patterson

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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