等额还款数学模型与计算Word文档下载推荐.docx
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等额还款数学模型与计算Word文档下载推荐.docx
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(5)
则
(1)-
(2)有:
(2)-(3)有:
(4)-(5)有:
贷款分
年还清,共
个月。
则有:
即
则:
所以:
每月还款
其中本金每月为
…,
利息每月为
,…,
总共还款
元
Matlab程序:
K=160000;
%贷款金额
m=5;
%还款年限
p=0.04032;
%年利率
r=p/12;
%月利率
n=m*12;
x=zeros(1,n);
%每月还本金
y=zeros(1,n);
%每月所剩本金
L=zeros(1,n);
%每月还利息
a=K*r*(1+r)^n/((1+r)^n-1);
%每月等额还款
L
(1)=K*r;
x
(1)=a-L
(1);
y
(1)=K-x
(1);
fori=2:
n
L(i)=y(i-1)*r;
x(i)=a-L(i);
y(i)=y(i-1)-x(i);
end
fprintf('
贷款%6d元,总共还款%5.2f元\n\n'
K,n*a);
月还款金额还本金还利息余本金\n'
);
fori=1:
%2d%5.2f%5.2f%5.2f%5.2f\n'
i,a,x(i),L(i),y(i));
如贷款16000元,分5年还清,年利率为4.032%,则计算结果如下(银行的还款计划表):
贷款160000元,总共还款176937.28元
月还款金额还本金还利息余本金
12948.952411.35537.60157588.65
22948.952419.46529.50155169.19
32948.952427.59521.37152741.60
42948.952435.74513.21150305.86
52948.952443.93505.03147861.93
62948.952452.14496.82145409.79
72948.952460.38488.58142949.42
82948.952468.64480.31140480.77
92948.952476.94472.02138003.83
102948.952485.26463.69135518.57
112948.952493.61455.34133024.96
122948.952501.99446.96130522.97
132948.952510.40438.56128012.57
142948.952518.83430.12125493.74
152948.952527.30421.66122966.44
162948.952535.79413.17120430.66
172948.952544.31404.65117886.35
182948.952552.86396.10115333.49
192948.952561.43387.52112772.06
202948.952570.04378.91110202.02
212948.952578.68370.28107623.34
222948.952587.34361.61105036.00
232948.952596.03352.92102439.97
242948.952604.76344.2099835.21
252948.952613.51335.4597221.70
262948.952622.29326.6694599.41
272948.952631.10317.8591968.31
282948.952639.94309.0189328.37
292948.952648.81300.1486679.56
302948.952657.71291.2484021.85
312948.952666.64282.3181355.21
322948.952675.60273.3578679.61
332948.952684.59264.3675995.01
342948.952693.61255.3473301.40
352948.952702.66246.2970598.74
362948.952711.74237.2167887.00
372948.952720.85228.1065166.14
382948.952730.00218.9662436.15
392948.952739.17209.7959696.98
402948.952748.37200.5856948.61
412948.952757.61191.3554191.00
422948.952766.87182.0851424.13
432948.952776.17172.7948647.96
442948.952785.50163.4645862.46
452948.952794.86154.1043067.60
462948.952804.25144.7140263.35
472948.952813.67135.2837449.68
482948.952823.12125.8334626.56
492948.952832.61116.3531793.95
502948.952842.13106.8328951.82
512948.952851.6897.2826100.15
522948.952861.2687.7023238.89
532948.952870.8778.0820368.02
542948.952880.5268.4417487.50
552948.952890.2058.7614597.30
562948.952899.9149.0511697.40
572948.952909.6539.308787.74
582948.952919.4329.535868.32
592948.952929.2419.722939.08
602948.952939.089.880.00
方案二:
每月等额还本金方式
设月还本金相等,为
则
月利率
则第一月还利息
,总还款
则第二月还利息
月还利息
年总共还利息
=
总还款
Matlab程序为
%每月还总共的钱
b=K/n;
L(i)=(K-(i-1)*b)*r;
x(i)=b+L(i);
%每月总还钱
y(i)=K-i*b;
%余本金
s1=sum(L);
%总共利息
s2=(12*m*K-6*m*(12*m-1)*b)*r;
Total=K+s1;
%总共还款
K,Total);
i,x(i),b,L(i),y(i));
如贷款16000元,分5年还清,年利率为4.032%,则计算结果如下:
贷款160000元,总共还款176396.80元
13204.272666.67537.60157333.33
23195.312666.67528.64154666.67
33186.352666.67519.68152000.00
43177.392666.67510.72149333.33
53168.432666.67501.76146666.67
63159.472666.67492.80144000.00
73150.512666.67483.84141333.33
83141.552666.67474.88138666.67
93132.592666.67465.92136000.00
103123.632666.67456.96133333.33
113114.672666.67448.00130666.67
123105.712666.67439.04128000.00
133096.752666.67430.08125333.33
143087.792666.67421.12122666.67
153078.832666.67412.16120000.00
163069.872666.67403.20117333.33
173060.912666.67394.24114666.67
183051.952666.67385.28112000.00
193042.992666.67376.32109333.33
203034.032666.67367.36106666.67
213025.072666.67358.40104000.00
223016.112666.67349.44101333.33
233007.152666.67340.4898666.67
242998.192666.67331.5296000.00
252989.232666.67322.5693333.33
262980.272666.67313.6090666.67
272971.312666.67304.6488000.00
282962.352666.67295.6885333.33
292953.392666.67286.7282666.67
302944.432666.67277.7680000.00
312935.472666.67268.8077333.33
322926.512666.67259.8474666.67
332917.552666.67250.8872000.00
342908.592666.67241.9269333.33
352899.632666.67232.9666666.67
362890.672666.67224.0064000.00
372881.712666.67215.0461333.33
382872.752666.67206.0858666.67
392863.792666.67197.1256000.00
402854.832666.67188.1653333.33
412845.872666.67179.2050666.67
422836.912666.67170.2448000.00
432827.952666.67161.2845333.33
442818.992666.67152.3242666.67
452810.032666.67143.3640000.00
462801.072666.67134.4037333.33
472792.112666.67125.4434666.67
482783.152666.67116.4832000.00
492774.192666.67107.5229333.33
502765.232666.6798.5626666.67
512756.272666.6789.6024000.00
522747.312666.6780.6421333.33
532738.352666.6771.6818666.67
542729.392666.6762.7216000.00
552720.432666.6753.7613333.33
562711.472666.6744.8010666.67
572702.512666.6735.848000.00
582693.552666.6726.885333.33
592684.592666.6717.922666.67
602675.632666.678.960.00
如贷款16000元,分5年还清,年利率为4.032%,两种方案对比结果:
合成Matlab程序
%方案一:
每月等额还钱
x1=zeros(1,n);
y1=zeros(1,n);
L1=zeros(1,n);
L1
(1)=K*r;
x1
(1)=a-L1
(1);
y1
(1)=K-x1
(1);
L1(i)=y1(i-1)*r;
x1(i)=a-L1(i);
y1(i)=y1(i-1)-x1(i);
Total1=n*a;
%总共还钱
%方式2:
每月等额还本金
x2=zeros(1,n);
y2=zeros(1,n);
L2=zeros(1,n);
L2(i)=(K-(i-1)*b)*r;
x2(i)=b+L2(i);
y2(i)=K-i*b;
s1=sum(L2);
Total2=K+s1;
贷款%6d元,方案一总共还款%5.2f元,方案二总共还款%5.2f元\n\n'
K,Total1,Total2);
方案一:
方案二:
\n'
月还款金额还本金还利息余本金还款金额还本金还利息余本金\n'
%2d%5.2f%5.2f%5.2f%5.2f%5.2f%5.2f%5.2f%5.2f\n'
i,a,x1(i),L1(i),y1(i),x2(i),b,L2(i),y2(i));
u=1:
12*m;
plot(u,y1,'
r'
u,y2,'
b'
计算结果:
贷款160000元,方案一总共还款176937.28元,方案二总共还款176396.80元
月还款金额还本金还利息余本金还款金额还本金还利息余本金
12948.952411.35537.60157588.653204.272666.67537.60157333.33
22948.952419.46529.50155169.193195.312666.67528.64154666.67
32948.952427.59521.37152741.603186.352666.67519.68152000.00
42948.952435.74513.21150305.863177.392666.67510.72149333.33
52948.952443.93505.03147861.933168.432666.67501.76146666.67
62948.952452.14496.82145409.793159.472666.67492.80144000.00
72948.952460.38488.58142949.423150.512666.67483.84141333.33
82948.952468.64480.31140480.773141.552666.67474.88138666.67
92948.952476.94472.02138003.833132.592666.67465.92136000.00
102948.952485.26463.69135518.573123.632666.67456.96133333.33
112948.952493.61455.34133024.963114.672666.67448.00130666.67
122948.952501.99446.96130522.973105.712666.67439.04128000.00
132948.952510.40438.56128012.573096.752666.67430.08125333.33
142948.952518.83430.12125493.743087.792666.67421.12122666.67
152948.952527.30421.66122966.443078.832666.67412.16120000.00
162948.952535.79413.17120430.663069.872666.67403.20117333.33
172948.952544.31404.65117886.353060.912666.67394.24114666.67
182948.952552.86396.10115333.493051.952666.67385.28112000.00
192948.952561.43387.52112772.063042.992666.67376.32109333.33
202948.952570.04378.91110202.023034.032666.67367.36106666.67
212948.952578.68370.28107623.343025.072666.67358.40104000.00
222948.952587.34361.61105036.003016.112666.67349.44101333.33
232948.952596.03352.92102439.973007.152666.67340.4898666.67
242948.952604.76344.2099835.212998.192666.67331.5296000.00
252948.952613.51335.4597221.702989.232666.67322.5693333.33
262948.952622.29326.6694599.412980.272666.67313.6090666.67
272948.952631.10317.8591968.312971.312666.67304.6488000.00
282948.952639.94309.0189328.372962.352666.67295.6885333.33
292948.952648.81300.1486679.562953.392666.67286.7282666.67
302948.952657.71291.2484021.852944.432666.67277.7680000.00
312948.952666.64282.3181355.212935.472666.67268.8077333.33
322948.952675.60273.3578679.612926.512666.67259.8474666.67
332948.952684.59264.3675995.012917.552666.67250.8872000.00
342948.952693.61255.3473301.402908.592666.67241.9269333.33
352948.952702.66246.2970598.742899.632666.67232.9666666.67
362948.952711.74237.2167887.002890.672666.67224.0064000.00
372948.952720.85228.1065166.142881.712666.67215.0461333.33
382948.952730.00218.9662436.152872.752666.67206.0858666.67
392948.952739.17209.7959696.982863.792666.67197.1256000.00
402948.952748.37200.5856948.612854.832666.67188.1653333.33
412948.952757.61191.3554191.002845.872666.67179.2050666.67
422948.952766.87182.0851424.132836.912666.67170.2448000.00
432948.952776.17172.7948647.962827.952666.67161.2845333.33
442948.952785.50163.4645862.462818.992666.67152.3242666.67
452948.952794.86154.1043067.602810.032666.67143.3640000.00
462948.952804.25144.7140263.352801.072666.67134.4037333.33
472948.952813.67135.2837449.682792.112666.67125.4434666.67
482948.952823.12125.8334626.562783.152666.67116.4832000.00
492948.952832.61116.3531793.952774.192666.67107.5229333.33
502948.952842.13106.8328951.822765.232666.6798.5626666.67
512948.952851.6897.2826100.152756.272666.6789.6024000.00
522948.952861.2687.7023238.892747.312666.6780.6421333.33
532948.952870.8778.0820368.022738.352666.6771.6818666.67
542948.952880.5268.4417487.502729.392666.6762.7216000.00
552948.952890.2058.7614597.302720.432666.6753.7613333.33
562948.952899.9149.0511697.402711.472666.6744.8010666.67
572948.952909.6539.308787.742702.512666.6735.848000.00
582948.952919.4329.535868.322693.552666.6726.885333.33
592948.952929.2419.722939.082684.592666.67
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