TVM formula error in programming manual?

[Thomas Klemm]

(10-30-2023 08:18 PM)rprosperi Wrote:  Not a math issue, just a sign convention issue.

The formula is correct in the Owner's Manual on page 192:

\(
\begin{align}
0=PV+(1+ip)PMT\left[\frac{1-(1+i)^{-N}}{i}\right ]+FV(1+i)^{-N}
\end{align}
\)

The formula is wrong in the Programming Examples and Techniques on page 92:

\(
\begin{align}
0=-PV+(1+ip)PMT\left[\frac{1-(1+i)^{-N}}{i}\right ]+FV(1+i)^{-N}
\end{align}
\)

The formula is correct in the Programming Examples and Techniques on page 93:

\(
\begin{align}
PV=-(1+ip)PMT\left[\frac{1-(1+i)^{-N}}{i}\right ]-FV(1+i)^{-N}
\end{align}
\)

---

From page 192 of the Owner's Manual:

Quote:The correct sign (positive or negative) for TVM numbers is essential. The calculations will make
sense only if you consistently show payments out as negative and payments in (receipts) as positive.
Perform a calculation from the point of view of either the lender (investor) or the borrower, but not both!