发布时间 : 星期六 文章购房策略问题 - 图文更新完毕开始阅读5d952bef856a561252d36fbd
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 9687.539 9624.147 9560.453 9496.454 9432.149 9367.536 9302.615 9237.383 9171.839 9105.982 9039.81 8973.321 8906.515 8839.389 8771.943 8704.174 8636.08 8567.662 8498.916 8429.841 8360.436 8290.7 8220.63 8150.225 8079.483 8008.403 7936.983 7865.222 7793.117 7720.668 7647.873 7574.729 7501.236 7427.391 7353.193 6900.497 0.004781 32.993 86 3527.59 6823.78 0.004781 32.6262 87 3434.746 6746.696 0.004781 32.25764 88 3341.458 6669.244 0.004781 31.88732 89 3247.725 6591.421 0.004781 31.51523 90 3153.543 6513.226 0.004781 31.14136 91 3058.911 6434.658 0.004781 30.76571 92 2963.826 6355.713 0.004781 30.38825 93 2868.287 6276.392 0.004781 30.009 94 2772.291 6196.691 0.004781 29.62793 95 2675.836 6116.609 0.004781 29.24503 96 2578.92 6036.144 0.004781 28.86031 97 2481.54 5955.294 0.004781 28.47375 98 2383.695 5874.058 0.004781 28.08534 99 2285.382 5792.433 0.004781 27.69507 100 2186.599 5710.418 0.004781 27.30294 101 2087.344 5628.011 0.004781 26.90893 102 1987.614 5545.21 0.004781 26.51303 103 1887.407 5462.013 0.004781 26.11525 104 1786.721 5378.418 0.004781 25.71556 105 1685.554 5294.424 0.004781 25.31396 106 1583.903 5210.028 0.004781 24.91044 107 1481.766 5125.228 0.004781 24.505 108 1379.141 5040.023 0.004781 24.09761 109 1276.025 4954.411 0.004781 23.68828 110 1172.416 4868.389 0.004781 23.27699 111 1068.312 4781.956 0.004781 22.86373 112 963.7094 4695.11 0.004781 22.44849 113 858.6072 4607.848 0.004781 22.03127 114 753.0024 4520.17 0.004781 21.61206 115 646.8927 4432.072 0.004781 21.19084 116 540.2756 4343.552 0.004781 20.76761 117 433.1488 4254.61 0.004781 20.34235 118 325.5098 4165.242 0.004781 19.91507 119 217.3562 4075.447 0.004781 19.48573 120 108.6854 通过以上表格可以得出：总共向银行还款为13464.695元。逐月被银行拿走的利息见上表1
模型二： 购房与商贷快速计算模型
我们以利息最小化为目标函数，建立了首付以及月还款额、还款总额的约束条件利用了lingo软件对其进行求解，使模型具有了实际应用价值。
模型建立如下：
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0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 0.004781 46.31855 46.01545 45.71092 45.40492 45.09746 44.78853 44.47813 44.16624 43.85286 43.53798 43.22159 42.90369 42.58428 42.26333 41.94085 41.61683 41.29126 40.96413 40.63544 40.30518 39.97334 39.63991 39.30489 38.96826 38.63003 38.29018 37.9487 37.60559 37.26084 36.91444 36.56639 36.21667 35.86528 35.51221 35.15745 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 16.86629 16.42238 15.97635 15.52818 15.07788 14.62542 14.17079 13.714 13.25502 12.79384 12.33046 11.86486 11.39704 10.92698 10.45468 9.980113 9.503279 9.024166 8.542762 8.059056 7.573037 7.084695 6.594018 6.100994 5.605614 5.107865 4.607736 4.105216 3.600293 3.092956 2.583193 2.070993 1.556344 1.039234 0.519652
12bn(P?Q)(1?a)nminZ??(P?Q) n(1?b)?120%P?Q?N
(P?Q)(1?a)n?M n(1?b)?112bn(P?Q)(1?a)n P?Q?n(1?b)?112bn(P?Q)(1?a)n?(P?Q)(1?a)n n(1?b)?112bn(P?Q)(1?a)n表示还款的本息和 n(1?b)?1(P?Q)表示贷款额
(P?Q)(1?a)n采用年利率计算方式还款的本息和
代入数据：P=436050元
a=5.508%
b=0.459%
N=150000元 M=6600元
利用lingo软件求解结果如下：（过程见附录4）
n=5 m=5997.85元 c=120000元
也就是说王先生需要贷款额为316050元，年限五年每月还款额为6000元，他的家庭每
月开销上限为2100元
模型三： 购房新方案模型
为了解决这一问题，我们构造了这一模型：为使使两家人都满意。我们打算把王先生的无息款项，借一部分给他外甥，让他外甥能购买房，并且所付利息不是较多，同时
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让他外甥，在现有的能力下，在能够把每月的房贷还清的同时，还能够向王先生还部分钱，是王先生把这部分钱用来还自己的房贷，这种方案使王先生最终所付的房贷利息比他准备把无息款项用来一次性提前还款的方案较少。
模型具体求解如下：
假设王先生把无息款项17000元（不包括年终奖30000元）用来提起还款，那么以后他还一共需要付利息5175.927元，求解过程见表格：
表2.王先生每月还款数额和利息 共需还款额 月利率 利息 每月还款数 110050 0.00459 505.1295 6000 104555.1 0.00459 479.908 6000 99035.04 0.00459 454.5708 6000 93489.61 0.00459 429.1173 6000 87918.73 0.00459 403.547 6000 82322.27 0.00459 377.8592 6000 76700.13 0.00459 352.0536 6000 71052.19 0.00459 326.1295 6000 65378.31 0.00459 300.0865 6000 59678.4 0.00459 273.9239 6000 53952.33 0.00459 247.6412 6000 48199.97 0.00459 221.2378 6000 42421.2 0.00459 194.7133 6000 36615.92 0.00459 168.0671 6000 30783.98 0.00459 141.2985 6000 24925.28 0.00459 114.407 6000 19039.69 0.00459 87.39218 6000 13127.08 0.00459 60.25331 6000 7187.336 0.00459 32.98987 6000 1220.326 0.00459 5.601295 6000 总共还款利息 5175.927
D?0.459%?(125746.9?d)?(125746.9?6000?d)?(125746.9?12000?d)???(125746.9?6000n?d)?
0?(125746.9?6000n?d)?6000
30000?d?150000 B=5175.927-D
b(150000?d)(1?a)n y?12n(1?b)?11500?E?d?y?2000 54ddd(1?0.459%)54?(1?0.459%)53???(1?0.459%)?d 545454
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E?B
我们采用了代入排除的方法得出了d
d=30000
外甥A向王先生借30000元，每月向王先生还款500元直至所借钱还清为止，并且外甥A还需还房贷1316元，也就是说外甥A的家庭开销上限为1700
具体数据求解见表格3、4：
表3.外甥A每月还款数额和利息 每月每月月月贷款数额 月利率 利息 还款贷款数额 月利率 利息 还款份 份 数 数 1 120000 0.004781 573.75 1316 31 96117.57 0.004781 459.56 1316 2 119257.8 0.004781 570.20 1316 32 95261.13 0.004781 455.47 1316 3 118512 0.004781 566.64 1316 33 94400.6 0.004781 451.35 1316 4 117762.6 0.004781 563.05 1316 34 93535.95 0.004781 447.22 1316 5 117009.6 0.004781 559.45 1316 35 92667.17 0.004781 443.06 1316 6 116253.1 0.004781 555.84 1316 36 91794.23 0.004781 438.89 1316 7 115492.9 0.004781 552.20 1316 37 90917.12 0.004781 434.70 1316 8 114729.1 0.004781 548.55 1316 38 90035.82 0.004781 430.48 1316 9 113961.7 0.004781 544.88 1316 39 89150.3 0.004781 426.25 1316 10 113190.6 0.004781 541.19 1316 40 88260.55 0.004781 422.00 1316 11 112415.7 0.004781 537.49 1316 41 87366.55 0.004781 417.72 1316 12 111637.2 0.004781 533.77 1316 42 86468.27 0.004781 413.43 1316 13 110855 0.004781 530.03 1316 43 85565.7 0.004781 409.11 1316 14 110069 0.004781 526.27 1316 44 84658.81 0.004781 404.77 1316 15 109279.3 0.004781 522.49 1316 45 83747.58 0.004781 400.42 1316 16 108485.8 0.004781 518.70 1316 46 82832 0.004781 396.04 1316 17 107688.5 0.004781 514.89 1316 47 81912.04 0.004781 391.64 1316 18 106887.4 0.004781 511.06 1316 48 80987.68 0.004781 387.22 1316 19 106082.4 0.004781 507.21 1316 49 80058.91 0.004781 382.78 1316 20 105273.6 0.004781 503.34 1316 50 79125.69 0.004781 378.32 1316 21 104461 0.004781 499.45 1316 51 78188.01 0.004781 373.84 1316 22 103644.4 0.004781 495.55 1316 52 77245.84 0.004781 369.33 1316 23 102824 0.004781 491.63 1316 53 76299.18 0.004781 364.81 1316 24 101999.6 0.004781 487.69 1316 54 75347.98 0.004781 360.26 1316 25 101171.3 0.004781 483.73 1316 55 74392.24 0.004781 355.69 1316 26 100339 0.004781 479.75 1316 56 73431.93 0.004781 351.10 1316 27 99502.76 0.004781 475.75 1316 57 72467.02 0.004781 346.48 1316 28 98662.5 0.004781 471.73 1316 58 71497.51 0.004781 341.85 1316 29 97818.23 0.004781 467.69 1316 59 70523.35 0.004781 337.19 1316 30 96969.93 0.004781 463.64 1316 60 69544.54 0.004781 332.51 1316
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