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a guest Jan 18th, 2019 64 Never
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  1. r' = r ^ (1/12), the monthly rate
  2. T' = 12 * T, the number of months
  3.    
  4. B(0) = P
  5. B(i + 1) = r' * B(i) - x
  6. B(T') = r' * B(T' - 1) - x = 0
  7.    
  8. i    B(i)
  9. 0    P
  10. 1    r'P - x
  11. 2    r'r'P - r'x - x
  12. 3    r'r'r'P - r'r'x - r'x - x
  13. ...
  14. k    (r' ^ k) * P - x * (r' ^ k - 1) / (r' - 1)
  15.    
  16. (r' ^ T') * P - x * (r' ^ T' - 1) / (r' - 1) = 0
  17. x = P * (r' ^ T') * (r' - 1) / (r' ^ T' - 1)
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