(11C) TVM for HP-11C

[Albert Chan]

A faster version of guess_i(), replaced sqrt() by its Pade approximation
This is also safer, avoided sqrt of negative number issue.

Code:

function guess_i(n, pv, pmt, fv)    -- cash-flow sign convention
    local a = (fv+pv)/n
    local b = (fv-pv)-a
    local c = (pmt+a)/b
    b = n*n*a*c/b                   -- I coef = [b/c/3, -2, 4c]
    return c * (b-3)/(b-1.5)        -- pade(4c/(1+sqrt(1-4b/3)),b,2,2)
end

lua> guess_i(12, 5000, -500, 0)
0.029199705714052143
lua> guess_i(12, 0, -400, 5000)
0.007391911604953607

Update: formula adjusted so fv+pv=0 will give i = pmt/fv, instead of NaN