(11C) TVM for HP-11C

[Albert Chan]

pv_i() and fv_i() are similar, we can combine them.

Just keep pv_i(), using previous post guess_i() for the guess.

Code:

function pv_i(n, a, i)              -- a = -pv/pmt
    i = i or guess_i(n, a, -1, 0)
    return function()
        local k = (1+i)^-n
        i = i - (a*i-(1-k)) / ((1-k)/i - k*n/(1+i))
        return i
    end
end

lua> g = pv_i(12, 5000/500)
lua> g(), g()
0.029228537101221044      0.029228540769133633

For fv_i() problems, where PV=0, add negative sign for the input.
In other words, fv_i(n, a) ≡ pv_i(-n, -a)

lua> g = pv_i(-12, -5000/400)
lua> g(), g()
0.007390622809688779      0.007390622804149185

This setup has another advantage, with invariant: sign(i) = sign(n-a)
For above examples, 12 > 10, -12 > -12.5, thus positive interest rate.

Update: numbers adjusted with updated guess_i()