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房贷计算的基本知识
送交者: 查理王 2012年12月07日11:55:50 于 [五 味 斋] 发送悄悄话

以在美国三十年固定利率房贷为例。

本金十万美元，年利4%，起始时间2012年1月1日。

利息计算的基本规则：

1.按月计息 

2.本金每月重算 

3. 当月利息次月付


计算每月付款额就是求得X 使得本金在三十年后归零。

具体公式很容易推导。

下面是具体计算结果，一目了然。


Original balance  $100,000 CPR
Mortgage rate 4.00% SMM
Beginning Monthly Interest Scheduled End
t Balance Payment Payment Principle Balance
1 100000.00 477.42 333.33 144.08 99855.92
2 99855.92 477.42 332.85 144.56 99711.36
3 99711.36 477.42 332.37 145.04 99566.31
4 99566.31 477.42 331.89 145.53 99420.78
5 99420.78 477.42 331.40 146.01 99274.77
6 99274.77 477.42 330.92 146.50 99128.27
7 99128.27 477.42 330.43 146.99 98981.28
8 98981.28 477.42 329.94 147.48 98833.81
9 98833.81 477.42 329.45 147.97 98685.84
10 98685.84 477.42 328.95 148.46 98537.37
11 98537.37 477.42 328.46 148.96 98388.42
12 98388.42 477.42 327.96 149.45 98238.96
13 98238.96 477.42 327.46 149.95 98089.01
14 98089.01 477.42 326.96 150.45 97938.56
15 97938.56 477.42 326.46 150.95 97787.61
16 97787.61 477.42 325.96 151.46 97636.15
17 97636.15 477.42 325.45 151.96 97484.19
18 97484.19 477.42 324.95 152.47 97331.72
19 97331.72 477.42 324.44 152.98 97178.74
20 97178.74 477.42 323.93 153.49 97025.26
21 97025.26 477.42 323.42 154.00 96871.26
22 96871.26 477.42 322.90 154.51 96716.75
23 96716.75 477.42 322.39 155.03 96561.72
24 96561.72 477.42 321.87 155.54 96406.18
25 96406.18 477.42 321.35 156.06 96250.12
26 96250.12 477.42 320.83 156.58 96093.54
27 96093.54 477.42 320.31 157.10 95936.43
28 95936.43 477.42 319.79 157.63 95778.81
29 95778.81 477.42 319.26 158.15 95620.65
30 95620.65 477.42 318.74 158.68 95461.97
31 95461.97 477.42 318.21 159.21 95302.77
32 95302.77 477.42 317.68 159.74 95143.03
33 95143.03 477.42 317.14 160.27 94982.75
34 94982.75 477.42 316.61 160.81 94821.95
35 94821.95 477.42 316.07 161.34 94660.61
36 94660.61 477.42 315.54 161.88 94498.73
37 94498.73 477.42 315.00 162.42 94336.31
38 94336.31 477.42 314.45 162.96 94173.35
39 94173.35 477.42 313.91 163.50 94009.84
40 94009.84 477.42 313.37 164.05 93845.79
41 93845.79 477.42 312.82 164.60 93681.20
42 93681.20 477.42 312.27 165.14 93516.05
43 93516.05 477.42 311.72 165.70 93350.36
44 93350.36 477.42 311.17 166.25 93184.11
45 93184.11 477.42 310.61 166.80 93017.31
46 93017.31 477.42 310.06 167.36 92849.95
47 92849.95 477.42 309.50 167.92 92682.03
48 92682.03 477.42 308.94 168.48 92513.56
49 92513.56 477.42 308.38 169.04 92344.52
50 92344.52 477.42 307.82 169.60 92174.92
51 92174.92 477.42 307.25 170.17 92004.76
52 92004.76 477.42 306.68 170.73 91834.02
53 91834.02 477.42 306.11 171.30 91662.72
54 91662.72 477.42 305.54 171.87 91490.85
55 91490.85 477.42 304.97 172.45 91318.40
56 91318.40 477.42 304.39 173.02 91145.38
57 91145.38 477.42 303.82 173.60 90971.78
58 90971.78 477.42 303.24 174.18 90797.61
59 90797.61 477.42 302.66 174.76 90622.85
60 90622.85 477.42 302.08 175.34 90447.51
61 90447.51 477.42 301.49 175.92 90271.59
62 90271.59 477.42 300.91 176.51 90095.08
63 90095.08 477.42 300.32 177.10 89917.98
64 89917.98 477.42 299.73 177.69 89740.29
65 89740.29 477.42 299.13 178.28 89562.01
66 89562.01 477.42 298.54 178.88 89383.14
67 89383.14 477.42 297.94 179.47 89203.66
68 89203.66 477.42 297.35 180.07 89023.60
69 89023.60 477.42 296.75 180.67 88842.93
70 88842.93 477.42 296.14 181.27 88661.65
71 88661.65 477.42 295.54 181.88 88479.78
72 88479.78 477.42 294.93 182.48 88297.29
73 88297.29 477.42 294.32 183.09 88114.20
74 88114.20 477.42 293.71 183.70 87930.50
75 87930.50 477.42 293.10 184.31 87746.19
76 87746.19 477.42 292.49 184.93 87561.26
77 87561.26 477.42 291.87 185.54 87375.72
78 87375.72 477.42 291.25 186.16 87189.55
79 87189.55 477.42 290.63 186.78 87002.77
80 87002.77 477.42 290.01 187.41 86815.36
81 86815.36 477.42 289.38 188.03 86627.33
82 86627.33 477.42 288.76 188.66 86438.67
83 86438.67 477.42 288.13 189.29 86249.39
84 86249.39 477.42 287.50 189.92 86059.47
85 86059.47 477.42 286.86 190.55 85868.92
86 85868.92 477.42 286.23 191.19 85677.73
87 85677.73 477.42 285.59 191.82 85485.91
88 85485.91 477.42 284.95 192.46 85293.45
89 85293.45 477.42 284.31 193.10 85100.35
90 85100.35 477.42 283.67 193.75 84906.60
91 84906.60 477.42 283.02 194.39 84712.21
92 84712.21 477.42 282.37 195.04 84517.16
93 84517.16 477.42 281.72 195.69 84321.47
94 84321.47 477.42 281.07 196.34 84125.13
95 84125.13 477.42 280.42 197.00 83928.13
96 83928.13 477.42 279.76 197.65 83730.48
97 83730.48 477.42 279.10 198.31 83532.16
98 83532.16 477.42 278.44 198.97 83333.19
99 83333.19 477.42 277.78 199.64 83133.55
100 83133.55 477.42 277.11 200.30 82933.25
101 82933.25 477.42 276.44 200.97 82732.27
102 82732.27 477.42 275.77 201.64 82530.63
103 82530.63 477.42 275.10 202.31 82328.32
104 82328.32 477.42 274.43 202.99 82125.33
105 82125.33 477.42 273.75 203.66 81921.67
106 81921.67 477.42 273.07 204.34 81717.33
107 81717.33 477.42 272.39 205.02 81512.30
108 81512.30 477.42 271.71 205.71 81306.59
109 81306.59 477.42 271.02 206.39 81100.20
110 81100.20 477.42 270.33 207.08 80893.12
111 80893.12 477.42 269.64 207.77 80685.35
112 80685.35 477.42 268.95 208.46 80476.88
113 80476.88 477.42 268.26 209.16 80267.72
114 80267.72 477.42 267.56 209.86 80057.87
115 80057.87 477.42 266.86 210.56 79847.31
116 79847.31 477.42 266.16 211.26 79636.05
117 79636.05 477.42 265.45 211.96 79424.09
118 79424.09 477.42 264.75 212.67 79211.42
119 79211.42 477.42 264.04 213.38 78998.05
120 78998.05 477.42 263.33 214.09 78783.96
121 78783.96 477.42 262.61 214.80 78569.16
122 78569.16 477.42 261.90 215.52 78353.64
123 78353.64 477.42 261.18 216.24 78137.40
124 78137.40 477.42 260.46 216.96 77920.45
125 77920.45 477.42 259.73 217.68 77702.76
126 77702.76 477.42 259.01 218.41 77484.36
127 77484.36 477.42 258.28 219.13 77265.22
128 77265.22 477.42 257.55 219.86 77045.36
129 77045.36 477.42 256.82 220.60 76824.76
130 76824.76 477.42 256.08 221.33 76603.43
131 76603.43 477.42 255.34 222.07 76381.36
132 76381.36 477.42 254.60 222.81 76158.55
133 76158.55 477.42 253.86 223.55 75935.00
134 75935.00 477.42 253.12 224.30 75710.70
135 75710.70 477.42 252.37 225.05 75485.65
136 75485.65 477.42 251.62 225.80 75259.85
137 75259.85 477.42 250.87 226.55 75033.30
138 75033.30 477.42 250.11 227.30 74806.00
139 74806.00 477.42 249.35 228.06 74577.94
140 74577.94 477.42 248.59 228.82 74349.12
141 74349.12 477.42 247.83 229.58 74119.53
142 74119.53 477.42 247.07 230.35 73889.18
143 73889.18 477.42 246.30 231.12 73658.06
144 73658.06 477.42 245.53 231.89 73426.17
145 73426.17 477.42 244.75 232.66 73193.51
146 73193.51 477.42 243.98 233.44 72960.08
147 72960.08 477.42 243.20 234.22 72725.86
148 72725.86 477.42 242.42 235.00 72490.87
149 72490.87 477.42 241.64 235.78 72255.09
150 72255.09 477.42 240.85 236.57 72018.52
151 72018.52 477.42 240.06 237.35 71781.17
152 71781.17 477.42 239.27 238.14 71543.02
153 71543.02 477.42 238.48 238.94 71304.08
154 71304.08 477.42 237.68 239.74 71064.35
155 71064.35 477.42 236.88 240.53 70823.82
156 70823.82 477.42 236.08 241.34 70582.48
157 70582.48 477.42 235.27 242.14 70340.34
158 70340.34 477.42 234.47 242.95 70097.39
159 70097.39 477.42 233.66 243.76 69853.63
160 69853.63 477.42 232.85 244.57 69609.06
161 69609.06 477.42 232.03 245.39 69363.68
162 69363.68 477.42 231.21 246.20 69117.48
163 69117.48 477.42 230.39 247.02 68870.45
164 68870.45 477.42 229.57 247.85 68622.61
165 68622.61 477.42 228.74 248.67 68373.93
166 68373.93 477.42 227.91 249.50 68124.43
167 68124.43 477.42 227.08 250.33 67874.10
168 67874.10 477.42 226.25 251.17 67622.93
169 67622.93 477.42 225.41 252.01 67370.92
170 67370.92 477.42 224.57 252.85 67118.08
171 67118.08 477.42 223.73 253.69 66864.39
172 66864.39 477.42 222.88 254.53 66609.85
173 66609.85 477.42 222.03 255.38 66354.47
174 66354.47 477.42 221.18 256.23 66098.24
175 66098.24 477.42 220.33 257.09 65841.15
176 65841.15 477.42 219.47 257.94 65583.21
177 65583.21 477.42 218.61 258.80 65324.40
178 65324.40 477.42 217.75 259.67 65064.73
179 65064.73 477.42 216.88 260.53 64804.20
180 64804.20 477.42 216.01 261.40 64542.80
181 64542.80 477.42 215.14 262.27 64280.53
182 64280.53 477.42 214.27 263.15 64017.38
183 64017.38 477.42 213.39 264.02 63753.36
184 63753.36 477.42 212.51 264.90 63488.45
185 63488.45 477.42 211.63 265.79 63222.66
186 63222.66 477.42 210.74 266.67 62955.99
187 62955.99 477.42 209.85 267.56 62688.43
188 62688.43 477.42 208.96 268.45 62419.98
189 62419.98 477.42 208.07 269.35 62150.63
190 62150.63 477.42 207.17 270.25 61880.38
191 61880.38 477.42 206.27 271.15 61609.23
192 61609.23 477.42 205.36 272.05 61337.18
193 61337.18 477.42 204.46 272.96 61064.22
194 61064.22 477.42 203.55 273.87 60790.36
195 60790.36 477.42 202.63 274.78 60515.58
196 60515.58 477.42 201.72 275.70 60239.88
197 60239.88 477.42 200.80 276.62 59963.26
198 59963.26 477.42 199.88 277.54 59685.73
199 59685.73 477.42 198.95 278.46 59407.26
200 59407.26 477.42 198.02 279.39 59127.87
201 59127.87 477.42 197.09 280.32 58847.55
202 58847.55 477.42 196.16 281.26 58566.29
203 58566.29 477.42 195.22 282.19 58284.10
204 58284.10 477.42 194.28 283.13 58000.96
205 58000.96 477.42 193.34 284.08 57716.88
206 57716.88 477.42 192.39 285.03 57431.86
207 57431.86 477.42 191.44 285.98 57145.88
208 57145.88 477.42 190.49 286.93 56858.95
209 56858.95 477.42 189.53 287.89 56571.07
210 56571.07 477.42 188.57 288.85 56282.22
211 56282.22 477.42 187.61 289.81 55992.42
212 55992.42 477.42 186.64 290.77 55701.64
213 55701.64 477.42 185.67 291.74 55409.90
214 55409.90 477.42 184.70 292.72 55117.18
215 55117.18 477.42 183.72 293.69 54823.49
216 54823.49 477.42 182.74 294.67 54528.82
217 54528.82 477.42 181.76 295.65 54233.17
218 54233.17 477.42 180.78 296.64 53936.53
219 53936.53 477.42 179.79 297.63 53638.90
220 53638.90 477.42 178.80 298.62 53340.28
221 53340.28 477.42 177.80 299.61 53040.67
222 53040.67 477.42 176.80 300.61 52740.06
223 52740.06 477.42 175.80 301.62 52438.44
224 52438.44 477.42 174.79 302.62 52135.82
225 52135.82 477.42 173.79 303.63 51832.19
226 51832.19 477.42 172.77 304.64 51527.55
227 51527.55 477.42 171.76 305.66 51221.89
228 51221.89 477.42 170.74 306.68 50915.22
229 50915.22 477.42 169.72 307.70 50607.52
230 50607.52 477.42 168.69 308.72 50298.80
231 50298.80 477.42 167.66 309.75 49989.04
232 49989.04 477.42 166.63 310.79 49678.26
233 49678.26 477.42 165.59 311.82 49366.44
234 49366.44 477.42 164.55 312.86 49053.58
235 49053.58 477.42 163.51 313.90 48739.67
236 48739.67 477.42 162.47 314.95 48424.72
237 48424.72 477.42 161.42 316.00 48108.72
238 48108.72 477.42 160.36 317.05 47791.67
239 47791.67 477.42 159.31 318.11 47473.56
240 47473.56 477.42 158.25 319.17 47154.39
241 47154.39 477.42 157.18 320.23 46834.16
242 46834.16 477.42 156.11 321.30 46512.86
243 46512.86 477.42 155.04 322.37 46190.48
244 46190.48 477.42 153.97 323.45 45867.04
245 45867.04 477.42 152.89 324.53 45542.51
246 45542.51 477.42 151.81 325.61 45216.91
247 45216.91 477.42 150.72 326.69 44890.21
248 44890.21 477.42 149.63 327.78 44562.43
249 44562.43 477.42 148.54 328.87 44233.56
250 44233.56 477.42 147.45 329.97 43903.59
251 43903.59 477.42 146.35 331.07 43572.52
252 43572.52 477.42 145.24 332.17 43240.34
253 43240.34 477.42 144.13 333.28 42907.06
254 42907.06 477.42 143.02 334.39 42572.67
255 42572.67 477.42 141.91 335.51 42237.17
256 42237.17 477.42 140.79 336.62 41900.54
257 41900.54 477.42 139.67 337.75 41562.79
258 41562.79 477.42 138.54 338.87 41223.92
259 41223.92 477.42 137.41 340.00 40883.92
260 40883.92 477.42 136.28 341.14 40542.78
261 40542.78 477.42 135.14 342.27 40200.51
262 40200.51 477.42 134.00 343.41 39857.10
263 39857.10 477.42 132.86 344.56 39512.54
264 39512.54 477.42 131.71 345.71 39166.83
265 39166.83 477.42 130.56 346.86 38819.97
266 38819.97 477.42 129.40 348.02 38471.96
267 38471.96 477.42 128.24 349.18 38122.78
268 38122.78 477.42 127.08 350.34 37772.44
269 37772.44 477.42 125.91 351.51 37420.94
270 37420.94 477.42 124.74 352.68 37068.26
271 37068.26 477.42 123.56 353.85 36714.40
272 36714.40 477.42 122.38 355.03 36359.37
273 36359.37 477.42 121.20 356.22 36003.15
274 36003.15 477.42 120.01 357.40 35645.75
275 35645.75 477.42 118.82 358.60 35287.15
276 35287.15 477.42 117.62 359.79 34927.36
277 34927.36 477.42 116.42 360.99 34566.37
278 34566.37 477.42 115.22 362.19 34204.17
279 34204.17 477.42 114.01 363.40 33840.77
280 33840.77 477.42 112.80 364.61 33476.16
281 33476.16 477.42 111.59 365.83 33110.33
282 33110.33 477.42 110.37 367.05 32743.28
283 32743.28 477.42 109.14 368.27 32375.01
284 32375.01 477.42 107.92 369.50 32005.51
285 32005.51 477.42 106.69 370.73 31634.78
286 31634.78 477.42 105.45 371.97 31262.82
287 31262.82 477.42 104.21 373.21 30889.61
288 30889.61 477.42 102.97 374.45 30515.16
289 30515.16 477.42 101.72 375.70 30139.46
290 30139.46 477.42 100.46 376.95 29762.51
291 29762.51 477.42 99.21 378.21 29384.31
292 29384.31 477.42 97.95 379.47 29004.84
293 29004.84 477.42 96.68 380.73 28624.11
294 28624.11 477.42 95.41 382.00 28242.10
295 28242.10 477.42 94.14 383.27 27858.83
296 27858.83 477.42 92.86 384.55 27474.28
297 27474.28 477.42 91.58 385.83 27088.44
298 27088.44 477.42 90.29 387.12 26701.32
299 26701.32 477.42 89.00 388.41 26312.91
300 26312.91 477.42 87.71 389.71 25923.21
301 25923.21 477.42 86.41 391.00 25532.20
302 25532.20 477.42 85.11 392.31 25139.89
303 25139.89 477.42 83.80 393.62 24746.28
304 24746.28 477.42 82.49 394.93 24351.35
305 24351.35 477.42 81.17 396.24 23955.11
306 23955.11 477.42 79.85 397.56 23557.54
307 23557.54 477.42 78.53 398.89 23158.65
308 23158.65 477.42 77.20 400.22 22758.43
309 22758.43 477.42 75.86 401.55 22356.88
310 22356.88 477.42 74.52 402.89 21953.98
311 21953.98 477.42 73.18 404.24 21549.75
312 21549.75 477.42 71.83 405.58 21144.17
313 21144.17 477.42 70.48 406.93 20737.23
314 20737.23 477.42 69.12 408.29 20328.94
315 20328.94 477.42 67.76 409.65 19919.29
316 19919.29 477.42 66.40 411.02 19508.27
317 19508.27 477.42 65.03 412.39 19095.88
318 19095.88 477.42 63.65 413.76 18682.12
319 18682.12 477.42 62.27 415.14 18266.98
320 18266.98 477.42 60.89 416.53 17850.45
321 17850.45 477.42 59.50 417.91 17432.54
322 17432.54 477.42 58.11 419.31 17013.23
323 17013.23 477.42 56.71 420.70 16592.53
324 16592.53 477.42 55.31 422.11 16170.42
325 16170.42 477.42 53.90 423.51 15746.91
326 15746.91 477.42 52.49 424.93 15321.98
327 15321.98 477.42 51.07 426.34 14895.64
328 14895.64 477.42 49.65 427.76 14467.88
329 14467.88 477.42 48.23 429.19 14038.69
330 14038.69 477.42 46.80 430.62 13608.07
331 13608.07 477.42 45.36 432.06 13176.01
332 13176.01 477.42 43.92 433.50 12742.52
333 12742.52 477.42 42.48 434.94 12307.58
334 12307.58 477.42 41.03 436.39 11871.19
335 11871.19 477.42 39.57 437.84 11433.34
336 11433.34 477.42 38.11 439.30 10994.04
337 10994.04 477.42 36.65 440.77 10553.27
338 10553.27 477.42 35.18 442.24 10111.03
339 10111.03 477.42 33.70 443.71 9667.32
340 9667.32 477.42 32.22 445.19 9222.13
341 9222.13 477.42 30.74 446.67 8775.46
342 8775.46 477.42 29.25 448.16 8327.29
343 8327.29 477.42 27.76 449.66 7877.63
344 7877.63 477.42 26.26 451.16 7426.48
345 7426.48 477.42 24.75 452.66 6973.82
346 6973.82 477.42 23.25 454.17 6519.65
347 6519.65 477.42 21.73 455.68 6063.96
348 6063.96 477.42 20.21 457.20 5606.76
349 5606.76 477.42 18.69 458.73 5148.04
350 5148.04 477.42 17.16 460.26 4687.78
351 4687.78 477.42 15.63 461.79 4225.99
352 4225.99 477.42 14.09 463.33 3762.66
353 3762.66 477.42 12.54 464.87 3297.79
354 3297.79 477.42 10.99 466.42 2831.37
355 2831.37 477.42 9.44 467.98 2363.39
356 2363.39 477.42 7.88 469.54 1893.85
357 1893.85 477.42 6.31 471.10 1422.75
358 1422.75 477.42 4.74 472.67 950.08
359 950.08 477.42 3.17 474.25 475.83
360 475.83 477.42 1.59 475.83 0.00

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