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Dec 17th, 2017
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  1. d = (p r1 (1 + r1)^m r2 (1 + r2)^n)/
  2. (-r1 + (1 + r2)^n (r1 + (-1 + (1 + r1)^m) r2))
  3.  
  4. d is the periodic payment
  5. p is the loan amount
  6. r1 is the periodic rate for the first m periods
  7. r2 is the periodic rate for the next n periods
  8.  
  9. p = 100,000
  10. r1 = 0.03
  11. m = 2
  12. r2 = 0.04
  13. n = 3
  14.  
  15. pv1 = d/(1 + r1)
  16. pv2 = d/((1 + r1) (1 + r1))
  17. pv3 = d/((1 + r1) (1 + r1) (1 + r2))
  18. pv4 = d/((1 + r1) (1 + r1) (1 + r2) (1 + r2))
  19. pv5 = d/((1 + r1) (1 + r1) (1 + r2) (1 + r2) (1 + r2))
  20.  
  21. p = ((1 + r1)^-m (1 + r2)^-n (-d r1 +
  22. d (1 + r2)^n (r1 + (-1 + (1 + r1)^m) r2)))/(r1 r2)
  23.  
  24. d = (p r1 (1 + r1)^m r2 (1 + r2)^n)/
  25. (-r1 + (1 + r2)^n (r1 + (-1 + (1 + r1)^m) r2))
  26.  
  27. ∴ d = 22078.67
  28.  
  29. p = 1,000,000
  30. r1 = (1 + 0.03)^(1/12) - 1 = 0.00246627
  31. m = 5*12 = 60
  32. r2 = (1 + 0.04)^(1/12) - 1 = 0.00327374
  33. n = (25 - 5)*12 = 240
  34.  
  35. p = 1,000,000
  36. r1 = 0.03/12 = 0.0025
  37. m = 5*12 = 60
  38. r2 = 0.04/12 = 0.00333333
  39. n = (25 - 5)*12 = 240
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