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)

Instead of looking at plots, lets look at reverted series of I, from C = N/P
More specifically, from u = (C-1)/(N+1)

From A Series of Interest, by David W. Cantrell

I = (2*u)*(1 - (N-1)/3*u * (1 - (2*N+1)/3*u * (1 - (11*N+7)/15*u * (1 - ...

Assume 2 terms of I is good enough for estimating true I
Assume N big enough, so that N+1 ≈ N-1 ≈ N
Let C = 1 + ε

I/(2u) ≈ 1 − (N/3) * (ε/N) = 1 − 1/3*ε
I/(2u/C) ≈ (1+ε) * (1-ε/3) ≈ 1 + 2/3*ε

Rate guess, p version is (2u), n version is (2u/C), rel error ratio ≈ -2      QED