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# Untitled

a guest Feb 20th, 2019 66 Never
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1. [Present Value Annuity Due][1] = 33.61 x (1 + 0.010416667) x { 1 - 1/(1 + 0.010416667)^36 }/0.010416667
2. = 33.61 x 1.010416667 x { 1 - 1/(1.010416667)^36 }/0.010416667
3. = 33.61 x 1.010416667 x { 1 - 1/1.45217196873 }/0.010416667
4. = 33.61 x 1.010416667 x { 1 - 0.688623676487 }/0.010416667
5. = 33.61 x 1.010416667 x { 0.311376323513/0.010416667 }
6. = 33.61 x 1.010416667 x 29.8921261007
7. = 33.61 x 30.2035024242
9.
10. A' = PVAD / (1+i)
11. A' = 1015.14 / 1.010416667
12. A' = \$1,004.67
13.
14. Present Value Annuity Due = 33.61 x (1 + 0.0105) x { 1 - 1/(1 + 0.0105)^36 }/0.0105
15. = 33.61 x 1.0105 x { 1 - 1/(1.0105)^36 }/0.0105
16. = 33.61 x 1.0105 x { 1 - 1/1.45648978356 }/0.0105
17. = 33.61 x 1.0105 x { 1 - 0.68658222755 }/0.0105
18. = 33.61 x 1.0105 x { 0.31341777245/0.0105 }
19. = 33.61 x 1.0105 x 29.8493116619
20. = 33.61 x 30.1627294344
22.
23. A'' = PVAD / (1+i)
24. A'' = 1013.77 / 1.0105
25. A'' = \$1,003.23
26.
27. Newton Raphson Method IRR Calculation with TVM equation = 0
28.
29. TVM Eq. 1: PV(1+i)^N + PMT(1+i*type)[(1+i)^N -1]/i + FV = 0
30.
31. f(i) = 0 + 33.61 * (1 + i * 0) [(1+i)^36 - 1)]/i + -1000 * (1+i)^36
32.
33. f'(i) = (33.61 * ( 36 * i * (1 + i)^(35+0) - (1 + i)^36) + 1) / (i * i)) + 36 * -1000 * (1+0.1)^35
34.
35. i0 = 0.1
36. f(i1) = -20859.0286
37. f'(i1) = -772196.0009
38. i1 = 0.1 - -20859.0286/-772196.0009 = 0.0729873910496
39. Error Bound = 0.0729873910496 - 0.1 = 0.027013 > 0.000001
40.
41. i1 = 0.0729873910496
42. f(i2) = -7274.5413
43. f'(i2) = -301995.7711
44. i2 = 0.0729873910496 - -7274.5413/-301995.7711 = 0.0488991687999
45. Error Bound = 0.0488991687999 - 0.0729873910496 = 0.024088 > 0.000001
46.
47. i2 = 0.0488991687999
48. f(i3) = -2431.1344
49. f'(i3) = -124187.6435
50. i3 = 0.0488991687999 - -2431.1344/-124187.6435 = 0.0293228701788
51. Error Bound = 0.0293228701788 - 0.0488991687999 = 0.019576 > 0.000001
52.
53. i3 = 0.0293228701788
54. f(i4) = -732.3776
55. f'(i4) = -57078.0048
56. i4 = 0.0293228701788 - -732.3776/-57078.0048 = 0.0164917006907
57. Error Bound = 0.0164917006907 - 0.0293228701788 = 0.012831 > 0.000001
58.
59. i4 = 0.0164917006907
60. f(i5) = -167.5999
61. f'(i5) = -32858.4347
62. i5 = 0.0164917006907 - -167.5999/-32858.4347 = 0.0113910349433
63. Error Bound = 0.0113910349433 - 0.0164917006907 = 0.005101 > 0.000001
64.
65. i5 = 0.0113910349433
66. f(i6) = -17.997
67. f'(i6) = -26021.5726
68. i6 = 0.0113910349433 - -17.997/-26021.5726 = 0.010699415611
69. Error Bound = 0.010699415611 - 0.0113910349433 = 0.000692 > 0.000001
70.
71. i6 = 0.010699415611
72. f(i7) = -0.288
73. f'(i7) = -25192.367
74. i7 = 0.010699415611 - -0.288/-25192.367 = 0.0106879831887
75. Error Bound = 0.0106879831887 - 0.010699415611 = 1.1E-5 > 0.000001
76.
77. i7 = 0.0106879831887
78. f(i8) = -0.0001
79. f'(i8) = -25178.8435
80. i8 = 0.0106879831887 - -0.0001/-25178.8435 = 0.0106879801183
81. Error Bound = 0.0106879801183 - 0.0106879831887 = 0 < 0.000001
82.
83. IRR = 1.07%
84.
85.
86. Newton Raphson Method IRR Calculation with TVM equation = 0
87.
88. TVM Eq. 2: PV + PMT(1+i*type)[1-{(1+i)^-N}]/i + FV(1+i)^-N = 0
89.
90. f(i) = -1000 + 33.61 * (1 + i * 0) [1 - (1+i)^-36)]/i + 0 * (1+i)^-36
91.
92. f'(i) = (-33.61 * (1+i)^-36 * ((1+i)^36 - 36 * i - 1) /(i*i)) + (0 * -36 * (1+i)^(-36-1))
93.
94. i0 = 0.1
95. f(i1) = -674.7726
96. f'(i1) = -2860.8622
97. i1 = 0.1 - -674.7726/-2860.8622 = -0.135863356364
98. Error Bound = -0.135863356364 - 0.1 = 0.235863 > 0.000001
99.
100. i1 = -0.135863356364
101. f(i2) = 46220.4067
102. f'(i2) = -1361282.2783
103. i2 = -0.135863356364 - 46220.4067/-1361282.2783 = -0.101909776386
104. Error Bound = -0.101909776386 - -0.135863356364 = 0.033954 > 0.000001
105.
106. i2 = -0.101909776386
107. f(i3) = 14472.9891
108. f'(i3) = -417070.1913
109. i3 = -0.101909776386 - 14472.9891/-417070.1913 = -0.0672082095036
110. Error Bound = -0.0672082095036 - -0.101909776386 = 0.034702 > 0.000001
111.
112. i3 = -0.0672082095036
113. f(i4) = 4620.5467
114. f'(i4) = -136713.9676
115. i4 = -0.0672082095036 - 4620.5467/-136713.9676 = -0.0334110286059
116. Error Bound = -0.0334110286059 - -0.0672082095036 = 0.033797 > 0.000001
117.
118. i4 = -0.0334110286059
119. f(i5) = 1412.836
120. f'(i5) = -50859.7324
121. i5 = -0.0334110286059 - 1412.836/-50859.7324 = -0.00563196002357
122. Error Bound = -0.00563196002357 - -0.0334110286059 = 0.027779 > 0.000001
123.
124. i5 = -0.00563196002357
125. f(i6) = 345.5376
126. f'(i6) = -24366.4494
127. i6 = -0.00563196002357 - 345.5376/-24366.4494 = 0.00854891782087
128. Error Bound = 0.00854891782087 - -0.00563196002357 = 0.014181 > 0.000001
129.
130. i6 = 0.00854891782087
131. f(i7) = 37.705
132. f'(i7) = -17208.0395
133. i7 = 0.00854891782087 - 37.705/-17208.0395 = 0.010740042325
134. Error Bound = 0.010740042325 - 0.00854891782087 = 0.002191 > 0.000001
135.
136. i7 = 0.010740042325
137. f(i8) = -0.8934
138. f'(i8) = -16335.3764
139. i8 = 0.010740042325 - -0.8934/-16335.3764 = 0.0106853483863
140. Error Bound = 0.0106853483863 - 0.010740042325 = 5.5E-5 > 0.000001
141.
142. i8 = 0.0106853483863
143. f(i9) = 0.0452
144. f'(i9) = -16356.5205
145. i9 = 0.0106853483863 - 0.0452/-16356.5205 = 0.0106881114105
146. Error Bound = 0.0106881114105 - 0.0106853483863 = 3.0E-6 > 0.000001
147.
148. i9 = 0.0106881114105
149. f(i10) = -0.0023
150. f'(i10) = -16355.4516
151. i10 = 0.0106881114105 - -0.0023/-16355.4516 = 0.010687973564
152. Error Bound = 0.010687973564 - 0.0106881114105 = 0 < 0.000001
153.
154. IRR = 1.07%
155.
156. sum(1/(1+.0104)**i for i in xrange(36)) == 30.2116668761916
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