TVM solve for interest rate, revisited

[Albert Chan]

This solved TVM calculations, 5 variables, 1 unknown

Code:

function tvm(n,i,pv,pmt,fv)
    if not pv then n,pv,pmt,fv = -n,fv,-pmt end
    if not fv then
        if i==0 then return -n*pmt - pv end
        local s = signbit(i*n)  -- force z > 0
        local z = expm1(log1p(i)*(s and -n or n))
        return s and (pmt/i*z-pv)/(1+z) or (-pmt/i-pv)*z-pv
    end
    local flip = abs(pv) > abs(fv)
    if flip then n,pv,fv = (n and -n),-fv,-pv end    
    if not pmt then
        if i==0 then return -(pv+fv)/n end
        return (-(pv+fv)/expm1(log1p(i)*n)-pv)*i
    elseif not i then
        i, n = find_rate(n,pv,pmt,fv)
        return n and i  -- false = no solution
    elseif not n then
        n = -(pv+fv)/(pmt+pv*i)
        if i ~= 0 then n = log1p(n*i)/log1p(i) end
        return flip and -n or n
    end
end

lua> n,pv,pmt,fv = 36, 30000, -550, -15000
lua> tvm(n,nil,pv,pmt,fv) -- i
0.005805072819420131
lua> i = _
lua> tvm(nil,i,pv,pmt,fv) -- n
36
lua> tvm(n,i,nil,pmt,fv) -- pv
30000
lua> tvm(n,i,pv,nil,fv) -- pmt
-550
lua> tvm(n,i,pv,pmt,nil) -- fv
-15000.000000000002