为什么没有显示var_a的原始值？

Question

基于对另一个StackExchange网站的一些研究，似乎以下程序应根据我对所提出的计算的理解显示var_a的原始值。但是，函数a似乎没有按预期计算a的值，并且我不清楚为什么会出现这种情况。在尝试正确解决var_a时应如何解决这个问题？

#! /usr/bin/env python3
import math


def main():
    var_n = 35      # thirty-five year investment
    var_iy = .04    # four percent interest per year
    var_pv = 30000  # thirty thousand dollar investment
    var_a = 12      # compounded twelve times per year
    var_fv = round(fv(var_n, var_iy, var_pv, var_a), 2)
    print('Future Value        =', var_fv)
    var_a = a(var_n, var_iy, var_pv, var_fv)
    print('Compounded Per Year =', var_a)


fv = lambda n, iy, pv, a: pv * (iy / a + 1) ** (n * a)


def a(n, iy, pv, fv):
    b = -math.log(fv / pv) / (iy * n)
    return (iy * b) / (lambert_w(b * math.exp(b)) - b)


def lambert_w(z, tolerance=1e-8):
    a = z
    while True:
        b = math.exp(a)
        c = a * b
        d = a - (c - z) / (c + b)
        if abs(a - d) <= tolerance:
            return a
        a = d


if __name__ == '__main__':
    main()

参考：How would you solve this equation for “A”?