TVM formula error in programming manual?

[Thomas Klemm]

As far as I understand the program "TMV2" the subroutine at LBL 10 is only used to calculate \(i\) and \(\mathit{MODE} = 1 + p \, i\).
With this the following formula is used to solve for \(N\) in the subroutine at LBL 01:

\(
\begin{align}
(1 + i)^N = \frac{\frac{\mathit{PMT}}{i} - \frac{\mathit{FV}}{1 + p \, i}}{\frac{\mathit{PMT}}{i} + \frac{\mathit{PV}}{1 + p \, i}}
\end{align}
\)

From here it's easy to solve for \(N\) using LN1+x and LN.

---

If you wonder how to come up with this equation, substitute:

\(
\begin{align}
a &= \mathit{PV} \\
\\
b &= \frac{(1 + p \, i)\,\mathit{PMT}}{i} \\
\\
c &= \mathit{FV} \\
\\
x &= (1 + i)^{-N} \\
\end{align}
\)

And then solve the following equation for \(x\):

\(
\begin{align}
0 = a + b \, (1 - x) + c \, x
\end{align}
\)

The solution is:

\(
\begin{align}
x = \frac{b + a}{b - c}
\end{align}
\)