Discount Rate

[Albert Chan]

(04-11-2022 03:11 PM)Albert Chan Wrote:  Plotting errors of both rate estimate, error(n version) ≈ -2 * error(p version)
In other words, this is much better rate estimate.

\(\displaystyle I_0 = \frac{2\;(N-P)}{N+1}
\left( \frac{{1 \over N} + {2 \over P}}{3} \right)
\)

Examples:

I₀(N= 36, P= 30) = .010210      // true rate = .010207
I₀(N=-36, P=-50) = .018074     // true rate = .017958

There are better ways to compensate the 1:2 error ratio.

I recently updated guess_i(n, pv, pmt, fv) that keep C series terms upto I^2
Converting it with FV=0, I1 = guess_i(N, P, -1, 0):

Rough estimate: \(\displaystyle I_0 = \frac{2\;(N-P)}{P(N+1)} \)

With correction: \(\displaystyle I_1
= I_0 \left( \frac{6 + 1\;(n-1)\;I_0}{6 + 2\;(n-1)\;I_0} \right)
= I_0 - \frac{I_0}{2 + \large \frac{6}{(N-1)\;I_0}} \)

Redo examples:

N= 36, P= 30     → I0 = .010811      → I1 = .010205
N=-36, P=-50    → I0 = .016000      → I1 = .017967