(15C) Halley's Method

[Albert Chan]

Hi, Gil

We just count sign changes, see Descartes rules of signs
N+1 Cash flows: [PV, PMT, ... , PMT, PMT+FV] = [6500, -1000, ..., -1000, 49000]

2 sign changes, thus 0 or 2 positive roots (for R = 1+i)
Based on rate edges, (PMT/FV , PMT/-PV) = (-1/50, 2/13)

2 Rates (if exist at all): -1/50 < i < 2/13

If we can show we have 1 root, we must have 2.