(11C) TVM for HP-11C

[Albert Chan]

(12-03-2020 05:53 PM)bshoring Wrote:  If I understand correctly, this program uses a modified Newton method to solve.

Yes !

Let a = (PV+FV)/(-PMT), using cash-flow sign-convention (results of post#3, LBL A)
We can interpret it as number of payments, if interest rate is zero.

Case FV=0: a*i/(1-k) = 1       → f(i) = a*i - (1-k) = 0       → f'(i) = a - k*n/(1+i)

Code:

function pv_i(n, a, i)
    i = i or 1/a - a/n^2
    return function()
        local k = (1+i)^-n
        i = i - (a*i-(1-k)) / ((1-k)/i - k*n/(1+i))
        return i
    end
end

Case PV=0: a*i/(K-1) = 1       → f(i) = a*i - (K-1) = 0       → f'(i) = a - K*n/(1+i)

Code:

function fv_i(n, a, i)
    i = i or 2*(a-n)/(a + (n-1)^2)
    return function()
        local K = (1+i)^n
        i = i - (a*i-(K-1)) / ((K-1)/i - K*n/(1+i))
        return i
    end
end

Iterations were setup with Newton's method.
But, denominator is not quite f'(i), resulting in better correction.

lua> g = pv_i(12, 5000/500) -- guess_i = 0.030555555555555558
lua> g(), g(), g()
0.02922075497755343        0.02922854050171087       0.029228540769134212

lua> g = fv_i(12, 5000/400) -- guess_i = 0.00749063670411985
lua> g(), g(), g()
0.007390656157378769      0.007390622804155507      0.007390622804147247