任务：计算等额本金还款和等额本息还款
小张贷款100万购买房子，贷款利率为4.9%（年利率），贷款期限20年。
1）用循环执行语句（for或者while），分别计算等额本金还款和等额本息还款的每月偿还本金、偿还利息、偿还本息、剩余本金
2）以数据框的形式给出。
3）计算两种还款方式的利息差额。
代码：
输入数据：
> #输入数据
> B <- 1000000
> R <- 0.049/12 #月利率
> t <- 20*12 #分t期还款
> N <- 1:t等额本金：
> #等额本金
> MBA <- B/t #每月偿还本金=贷款总额/贷款月数
> MYA <- B - MBA*(N-1) #每月剩余本金
> MIA <- MYA*R #每月偿还利息=剩余本金*月利率
> MPA <- MIA + MBA #每月偿还本息和
> one <- data.frame('等额本金每月偿还本金'=MBA,'等额本金每月偿还利息'=MIA,'等额本金每月偿还本息和'=MPA,'等额本金每月剩余本金'=MYA)
> one上述代码没有for循环语句，添加后如下：
> one <- data.frame('等额本金每月偿还本金'=0,'等额本金每月偿还利息'=0,'等额本金每月偿还本息和'=0,'等额本金每月剩余本金'=0)
> one
等额本金每月偿还本金 等额本金每月偿还利息 等额本金每月偿还本息和 等额本金每月剩余本金
1 0 0 0 0
> #等额本金
> MBA <- B/t #每月偿还本金=贷款总额/贷款月数
> for(i in N){
+ MYA <- B - MBA*(i-1) #每月剩余本金
+ MIA <- MYA*R #每月偿还利息=剩余本金*月利率
+ MPA <- MIA + MBA #每月偿还本息和
+ one[i,] <- data.frame('等额本金每月偿还本金'=MBA,'等额本金每月偿还利息'=MIA,'等额本金每月偿还本息和'=MPA,'等额本金每月剩余本金'=MYA)
+ }
> one
等额本金每月偿还本金 等额本金每月偿还利息 等额本金每月偿还本息和 等额本金每月剩余本金
1 4166.667 4083.33333 8250.000 1000000.000
2 4166.667 4066.31944 8232.986 995833.333
3 4166.667 4049.30556 8215.972 991666.667
4 4166.667 4032.29167 8198.958 987500.000
5 4166.667 4015.27778 8181.944 983333.333
......结果：
等额本金每月偿还本金 等额本金每月偿还利息 等额本金每月偿还本息和 等额本金每月剩余本金
1 4166.667 4083.33333 8250.000 1000000.000
2 4166.667 4066.31944 8232.986 995833.333
3 4166.667 4049.30556 8215.972 991666.667
4 4166.667 4032.29167 8198.958 987500.000
5 4166.667 4015.27778 8181.944 983333.333
6 4166.667 3998.26389 8164.931 979166.667
7 4166.667 3981.25000 8147.917 975000.000
8 4166.667 3964.23611 8130.903 970833.333
9 4166.667 3947.22222 8113.889 966666.667
10 4166.667 3930.20833 8096.875 962500.000
11 4166.667 3913.19444 8079.861 958333.333
12 4166.667 3896.18056 8062.847 954166.667
13 4166.667 3879.16667 8045.833 950000.000
14 4166.667 3862.15278 8028.819 945833.333
15 4166.667 3845.13889 8011.806 941666.667
16 4166.667 3828.12500 7994.792 937500.000
17 4166.667 3811.11111 7977.778 933333.333
18 4166.667 3794.09722 7960.764 929166.667
19 4166.667 3777.08333 7943.750 925000.000
20 4166.667 3760.06944 7926.736 920833.333
21 4166.667 3743.05556 7909.722 916666.667
22 4166.667 3726.04167 7892.708 912500.000
23 4166.667 3709.02778 7875.694 908333.333
24 4166.667 3692.01389 7858.681 904166.667
25 4166.667 3675.00000 7841.667 900000.000
26 4166.667 3657.98611 7824.653 895833.333
27 4166.667 3640.97222 7807.639 891666.667
28 4166.667 3623.95833 7790.625 887500.000
29 4166.667 3606.94444 7773.611 883333.333
30 4166.667 3589.93056 7756.597 879166.667
31 4166.667 3572.91667 7739.583 875000.000
32 4166.667 3555.90278 7722.569 870833.333
33 4166.667 3538.88889 7705.556 866666.667
34 4166.667 3521.87500 7688.542 862500.000
35 4166.667 3504.86111 7671.528 858333.333
36 4166.667 3487.84722 7654.514 854166.667
37 4166.667 3470.83333 7637.500 850000.000
38 4166.667 3453.81944 7620.486 845833.333
39 4166.667 3436.80556 7603.472 841666.667
40 4166.667 3419.79167 7586.458 837500.000
41 4166.667 3402.77778 7569.444 833333.333
42 4166.667 3385.76389 7552.431 829166.667
43 4166.667 3368.75000 7535.417 825000.000
44 4166.667 3351.73611 7518.403 820833.333
45 4166.667 3334.72222 7501.389 816666.667
46 4166.667 3317.70833 7484.375 812500.000
47 4166.667 3300.69444 7467.361 808333.333
48 4166.667 3283.68056 7450.347 804166.667
49 4166.667 3266.66667 7433.333 800000.000
50 4166.667 3249.65278 7416.319 795833.333
51 4166.667 3232.63889 7399.306 791666.667
52 4166.667 3215.62500 7382.292 787500.000
53 4166.667 3198.61111 7365.278 783333.333
54 4166.667 3181.59722 7348.264 779166.667
55 4166.667 3164.58333 7331.250 775000.000
56 4166.667 3147.56944 7314.236 770833.333
57 4166.667 3130.55556 7297.222 766666.667
58 4166.667 3113.54167 7280.208 762500.000
59 4166.667 3096.52778 7263.194 758333.333
60 4166.667 3079.51389 7246.181 754166.667
61 4166.667 3062.50000 7229.167 750000.000
62 4166.667 3045.48611 7212.153 745833.333
63 4166.667 3028.47222 7195.139 741666.667
64 4166.667 3011.45833 7178.125 737500.000
65 4166.667 2994.44444 7161.111 733333.333
66 4166.667 2977.43056 7144.097 729166.667
67 4166.667 2960.41667 7127.083 725000.000
68 4166.667 2943.40278 7110.069 720833.333
69 4166.667 2926.38889 7093.056 716666.667
70 4166.667 2909.37500 7076.042 712500.000
71 4166.667 2892.36111 7059.028 708333.333
72 4166.667 2875.34722 7042.014 704166.667
73 4166.667 2858.33333 7025.000 700000.000
74 4166.667 2841.31944 7007.986 695833.333
75 4166.667 2824.30556 6990.972 691666.667
76 4166.667 2807.29167 6973.958 687500.000
77 4166.667 2790.27778 6956.944 683333.333
78 4166.667 2773.26389 6939.931 679166.667
79 4166.667 2756.25000 6922.917 675000.000
80 4166.667 2739.23611 6905.903 670833.333
81 4166.667 2722.22222 6888.889 666666.667
82 4166.667 2705.20833 6871.875 662500.000
83 4166.667 2688.19444 6854.861 658333.333
84 4166.667 2671.18056 6837.847 654166.667
85 4166.667 2654.16667 6820.833 650000.000
86 4166.667 2637.15278 6803.819 645833.333
87 4166.667 2620.13889 6786.806 641666.667
88 4166.667 2603.12500 6769.792 637500.000
89 4166.667 2586.11111 6752.778 633333.333
90 4166.667 2569.09722 6735.764 629166.667
91 4166.667 2552.08333 6718.750 625000.000
92 4166.667 2535.06944 6701.736 620833.333
93 4166.667 2518.05556 6684.722 616666.667
94 4166.667 2501.04167 6667.708 612500.000
95 4166.667 2484.02778 6650.694 608333.333
96 4166.667 2467.01389 6633.681 604166.667
97 4166.667 2450.00000 6616.667 600000.000
98 4166.667 2432.98611 6599.653 595833.333
99 4166.667 2415.97222 6582.639 591666.667
100 4166.667 2398.95833 6565.625 587500.000
101 4166.667 2381.94444 6548.611 583333.333
102 4166.667 2364.93056 6531.597 579166.667
103 4166.667 2347.91667 6514.583 575000.000
104 4166.667 2330.90278 6497.569 570833.333
105 4166.667 2313.88889 6480.556 566666.667
106 4166.667 2296.87500 6463.542 562500.000
107 4166.667 2279.86111 6446.528 558333.333
108 4166.667 2262.84722 6429.514 554166.667
109 4166.667 2245.83333 6412.500 550000.000
110 4166.667 2228.81944 6395.486 545833.333
111 4166.667 2211.80556 6378.472 541666.667
112 4166.667 2194.79167 6361.458 537500.000
113 4166.667 2177.77778 6344.444 533333.333
114 4166.667 2160.76389 6327.431 529166.667
115 4166.667 2143.75000 6310.417 525000.000
116 4166.667 2126.73611 6293.403 520833.333
117 4166.667 2109.72222 6276.389 516666.667
118 4166.667 2092.70833 6259.375 512500.000
119 4166.667 2075.69444 6242.361 508333.333
120 4166.667 2058.68056 6225.347 504166.667
121 4166.667 2041.66667 6208.333 500000.000
122 4166.667 2024.65278 6191.319 495833.333
123 4166.667 2007.63889 6174.306 491666.667
124 4166.667 1990.62500 6157.292 487500.000
125 4166.667 1973.61111 6140.278 483333.333
126 4166.667 1956.59722 6123.264 479166.667
127 4166.667 1939.58333 6106.250 475000.000
128 4166.667 1922.56944 6089.236 470833.333
129 4166.667 1905.55556 6072.222 466666.667
130 4166.667 1888.54167 6055.208 462500.000
131 4166.667 1871.52778 6038.194 458333.333
132 4166.667 1854.51389 6021.181 454166.667
133 4166.667 1837.50000 6004.167 450000.000
134 4166.667 1820.48611 5987.153 445833.333
135 4166.667 1803.47222 5970.139 441666.667
136 4166.667 1786.45833 5953.125 437500.000
137 4166.667 1769.44444 5936.111 433333.333
138 4166.667 1752.43056 5919.097 429166.667
139 4166.667 1735.41667 5902.083 425000.000
140 4166.667 1718.40278 5885.069 420833.333
141 4166.667 1701.38889 5868.056 416666.667
142 4166.667 1684.37500 5851.042 412500.000
143 4166.667 1667.36111 5834.028 408333.333
144 4166.667 1650.34722 5817.014 404166.667
145 4166.667 1633.33333 5800.000 400000.000
146 4166.667 1616.31944 5782.986 395833.333
147 4166.667 1599.30556 5765.972 391666.667
148 4166.667 1582.29167 5748.958 387500.000
149 4166.667 1565.27778 5731.944 383333.333
150 4166.667 1548.26389 5714.931 379166.667
151 4166.667 1531.25000 5697.917 375000.000
152 4166.667 1514.23611 5680.903 370833.333
153 4166.667 1497.22222 5663.889 366666.667
154 4166.667 1480.20833 5646.875 362500.000
155 4166.667 1463.19444 5629.861 358333.333
156 4166.667 1446.18056 5612.847 354166.667
157 4166.667 1429.16667 5595.833 350000.000
158 4166.667 1412.15278 5578.819 345833.333
159 4166.667 1395.13889 5561.806 341666.667
160 4166.667 1378.12500 5544.792 337500.000
161 4166.667 1361.11111 5527.778 333333.333
162 4166.667 1344.09722 5510.764 329166.667
163 4166.667 1327.08333 5493.750 325000.000
164 4166.667 1310.06944 5476.736 320833.333
165 4166.667 1293.05556 5459.722 316666.667
166 4166.667 1276.04167 5442.708 312500.000
167 4166.667 1259.02778 5425.694 308333.333
168 4166.667 1242.01389 5408.681 304166.667
169 4166.667 1225.00000 5391.667 300000.000
170 4166.667 1207.98611 5374.653 295833.333
171 4166.667 1190.97222 5357.639 291666.667
172 4166.667 1173.95833 5340.625 287500.000
173 4166.667 1156.94444 5323.611 283333.333
174 4166.667 1139.93056 5306.597 279166.667
175 4166.667 1122.91667 5289.583 275000.000
176 4166.667 1105.90278 5272.569 270833.333
177 4166.667 1088.88889 5255.556 266666.667
178 4166.667 1071.87500 5238.542 262500.000
179 4166.667 1054.86111 5221.528 258333.333
180 4166.667 1037.84722 5204.514 254166.667
181 4166.667 1020.83333 5187.500 250000.000
182 4166.667 1003.81944 5170.486 245833.333
183 4166.667 986.80556 5153.472 241666.667
184 4166.667 969.79167 5136.458 237500.000
185 4166.667 952.77778 5119.444 233333.333
186 4166.667 935.76389 5102.431 229166.667
187 4166.667 918.75000 5085.417 225000.000
188 4166.667 901.73611 5068.403 220833.333
189 4166.667 884.72222 5051.389 216666.667
190 4166.667 867.70833 5034.375 212500.000
191 4166.667 850.69444 5017.361 208333.333
192 4166.667 833.68056 5000.347 204166.667
193 4166.667 816.66667 4983.333 200000.000
194 4166.667 799.65278 4966.319 195833.333
195 4166.667 782.63889 4949.306 191666.667
196 4166.667 765.62500 4932.292 187500.000
197 4166.667 748.61111 4915.278 183333.333
198 4166.667 731.59722 4898.264 179166.667
199 4166.667 714.58333 4881.250 175000.000
200 4166.667 697.56944 4864.236 170833.333
201 4166.667 680.55556 4847.222 166666.667
202 4166.667 663.54167 4830.208 162500.000
203 4166.667 646.52778 4813.194 158333.333
204 4166.667 629.51389 4796.181 154166.667
205 4166.667 612.50000 4779.167 150000.000
206 4166.667 595.48611 4762.153 145833.333
207 4166.667 578.47222 4745.139 141666.667
208 4166.667 561.45833 4728.125 137500.000
209 4166.667 544.44444 4711.111 133333.333
210 4166.667 527.43056 4694.097 129166.667
211 4166.667 510.41667 4677.083 125000.000
212 4166.667 493.40278 4660.069 120833.333
213 4166.667 476.38889 4643.056 116666.667
214 4166.667 459.37500 4626.042 112500.000
215 4166.667 442.36111 4609.028 108333.333
216 4166.667 425.34722 4592.014 104166.667
217 4166.667 408.33333 4575.000 100000.000
218 4166.667 391.31944 4557.986 95833.333
219 4166.667 374.30556 4540.972 91666.667
220 4166.667 357.29167 4523.958 87500.000
221 4166.667 340.27778 4506.944 83333.333
222 4166.667 323.26389 4489.931 79166.667
223 4166.667 306.25000 4472.917 75000.000
224 4166.667 289.23611 4455.903 70833.333
225 4166.667 272.22222 4438.889 66666.667
226 4166.667 255.20833 4421.875 62500.000
227 4166.667 238.19444 4404.861 58333.333
228 4166.667 221.18056 4387.847 54166.667
229 4166.667 204.16667 4370.833 50000.000
230 4166.667 187.15278 4353.819 45833.333
231 4166.667 170.13889 4336.806 41666.667
232 4166.667 153.12500 4319.792 37500.000
233 4166.667 136.11111 4302.778 33333.333
234 4166.667 119.09722 4285.764 29166.667
235 4166.667 102.08333 4268.750 25000.000
236 4166.667 85.06944 4251.736 20833.333
237 4166.667 68.05556 4234.722 16666.667
238 4166.667 51.04167 4217.708 12500.000
239 4166.667 34.02778 4200.694 8333.333
240 4166.667 17.01389 4183.681 4166.667
>等额本息：
> # 等额本息
> MPB <- B*R*(1+R)^t / ((1+R)^t-1) # 每月应还的等额本息，包含月还利息和月还本金
> MYBF <- function(n) # 如何将利息与本金分离出来
+ {
+ # 可知，MYB(n)为第n个月后剩余的欠银行的钱,即第n个月的剩余本金(n=1,2,3..)
+ # 那么MYB(N),N=0,1,2,...,且MYB(N)*r就是第N+1个月的利息
+ MYB <- B*(1+R)^n - MPB*((1+R)^n-1)/R
+ return(MYB)
+ }
> MYB <- MYBF(N-1) # 让时间从0,1,2,3...到n-1结束 #每月剩余本金
> MIB <- MYB * R # 月还利息
> MBB <- MPB - MIB # 月还本金
> two <- data.frame('等额本息每月偿还本金'=MBB,'等额本息每月偿还利息'=MIB,'等额本息每月偿还本息和'=MPB,'等额本金每月剩余本金'=MYB)
> two上述代码没有for循环语句，添加后如下：
> # 等额本息
> MPB <- B*R*(1+R)^t / ((1+R)^t-1) # 每月应还的等额本息，包含月还利息和月还本金
> two <- data.frame('等额本息每月偿还本金'=0,'等额本息每月偿还利息'=0,'等额本息每月偿还本息和'=0,'等额本息每月剩余本金'=0)
> two
等额本息每月偿还本金 等额本息每月偿还利息 等额本息每月偿还本息和 等额本息每月剩余本金
1 0 0 0 0
> MYBF <- function(n) # 如何将利息与本金分离出来
+ {
+ # 可知，MYB(n)为第n个月后剩余的欠银行的钱,即第n个月的剩余本金(n=1,2,3..)
+ # 那么MYB(N),N=0,1,2,...,且MYB(N)*r就是第N+1个月的利息
+ MYB <- B*(1+R)^n - MPB*((1+R)^n-1)/R
+ return(MYB)
+ }
> for(i in N-1){
+ MYB <- MYBF(i) # 让时间从0,1,2,3...到n-1结束 #每月剩余本金
+ MIB <- MYB * R # 月还利息
+ MBB <- MPB - MIB # 月还本金
+ two[i+1,] <- data.frame('等额本息每月偿还本金'=MBB,'等额本息每月偿还利息'=MIB,'等额本息每月偿还本息和'=MPB,'等额本金每月剩余本金'=MYB)
+
+ }
> two
等额本息每月偿还本金 等额本息每月偿还利息 等额本息每月偿还本息和 等额本息每月剩余本金
1 2461.107 4083.33333 6544.44 1000000.000
2 2471.157 4073.28381 6544.44 997538.893
3 2481.247 4063.19326 6544.44 995067.736
4 2491.379 4053.06150 6544.44 992586.489
5 2501.552 4042.88837 6544.44 990095.110
......结果：
等额本息每月偿还本金 等额本息每月偿还利息 等额本息每月偿还本息和 等额本金每月剩余本金
1 2461.107 4083.33333 6544.44 1000000.000
2 2471.157 4073.28381 6544.44 997538.893
3 2481.247 4063.19326 6544.44 995067.736
4 2491.379 4053.06150 6544.44 992586.489
5 2501.552 4042.88837 6544.44 990095.110
6 2511.767 4032.67369 6544.44 987593.558
7 2522.023 4022.41731 6544.44 985081.791
8 2532.321 4012.11905 6544.44 982559.768
9 2542.662 4001.77874 6544.44 980027.446
10 2553.044 3991.39620 6544.44 977484.785
11 2563.469 3980.97127 6544.44 974931.740
12 2573.937 3970.50377 6544.44 972368.271
13 2584.447 3959.99353 6544.44 969794.334
14 2595.000 3949.44037 6544.44 967209.887
15 2605.596 3938.84412 6544.44 964614.887
16 2616.236 3928.20460 6544.44 962009.291
17 2626.919 3917.52164 6544.44 959393.055
18 2637.645 3906.79506 6544.44 956766.136
19 2648.416 3896.02467 6544.44 954128.491
20 2659.230 3885.21031 6544.44 951480.075
21 2670.089 3874.35178 6544.44 948820.845
22 2680.992 3863.44892 6544.44 946150.756
23 2691.939 3852.50154 6544.44 943469.765
24 2702.931 3841.50945 6544.44 940777.826
25 2713.968 3830.47249 6544.44 938074.895
26 2725.050 3819.39045 6544.44 935360.927
27 2736.177 3808.26316 6544.44 932635.877
28 2747.350 3797.09044 6544.44 929899.699
29 2758.568 3785.87209 6544.44 927152.349
30 2769.833 3774.60794 6544.44 924393.781
31 2781.143 3763.29779 6544.44 921623.948
32 2792.499 3751.94146 6544.44 918842.805
33 2803.902 3740.53875 6544.44 916050.306
34 2815.351 3729.08949 6544.44 913246.405
35 2826.847 3717.59347 6544.44 910431.054
36 2838.390 3706.05051 6544.44 907604.207
37 2849.980 3694.46042 6544.44 904765.817
38 2861.617 3682.82300 6544.44 901915.837
39 2873.302 3671.13806 6544.44 899054.219
40 2885.035 3659.40541 6544.44 896180.917
41 2896.816 3647.62485 6544.44 893295.882
42 2908.644 3635.79619 6544.44 890399.066
43 2920.521 3623.91922 6544.44 887490.422
44 2932.447 3611.99376 6544.44 884569.900
45 2944.421 3600.01960 6544.44 881637.454
46 2956.444 3587.99655 6544.44 878693.033
47 2968.516 3575.92440 6544.44 875736.589
48 2980.638 3563.80296 6544.44 872768.073
49 2992.808 3551.63203 6544.44 869787.435
50 3005.029 3539.41139 6544.44 866794.627
51 3017.300 3527.14086 6544.44 863789.598
52 3029.620 3514.82022 6544.44 860772.298
53 3041.991 3502.44927 6544.44 857742.678
54 3054.413 3490.02780 6544.44 854700.687
55 3066.885 3477.55562 6544.44 851646.274
56 3079.408 3465.03251 6544.44 848579.389
57 3091.982 3452.45826 6544.44 845499.981
58 3104.608 3439.83266 6544.44 842407.999
59 3117.285 3427.15551 6544.44 839303.391
60 3130.014 3414.42660 6544.44 836186.106
61 3142.795 3401.64571 6544.44 833056.092
62 3155.628 3388.81263 6544.44 829913.297
63 3168.513 3375.92715 6544.44 826757.669
64 3181.451 3362.98905 6544.44 823589.156
65 3194.442 3349.99813 6544.44 820407.705
66 3207.486 3336.95415 6544.44 817213.262
67 3220.584 3323.85692 6544.44 814005.776
68 3233.734 3310.70620 6544.44 810785.192
69 3246.939 3297.50179 6544.44 807551.458
70 3260.197 3284.24345 6544.44 804304.519
71 3273.510 3270.93098 6544.44 801044.322
72 3286.876 3257.56415 6544.44 797770.813
73 3300.298 3244.14274 6544.44 794483.937
74 3313.774 3230.66653 6544.44 791183.639
75 3327.305 3217.13528 6544.44 787869.865
76 3340.892 3203.54879 6544.44 784542.560
77 3354.534 3189.90681 6544.44 781201.668
78 3368.231 3176.20913 6544.44 777847.134
79 3381.985 3162.45552 6544.44 774478.903
80 3395.795 3148.64575 6544.44 771096.918
81 3409.661 3134.77959 6544.44 767701.123
82 3423.584 3120.85680 6544.44 764291.462
83 3437.563 3106.87717 6544.44 760867.879
84 3451.600 3092.84045 6544.44 757430.315
85 3465.694 3078.74642 6544.44 753978.715
86 3479.846 3064.59484 6544.44 750513.021
87 3494.055 3050.38547 6544.44 747033.176
88 3508.322 3036.11808 6544.44 743539.120
89 3522.648 3021.79243 6544.44 740030.798
90 3537.032 3007.40828 6544.44 736508.150
91 3551.475 2992.96540 6544.44 732971.118
92 3565.977 2978.46354 6544.44 729419.643
93 3580.538 2963.90247 6544.44 725853.666
94 3595.159 2949.28194 6544.44 722273.128
95 3609.839 2934.60171 6544.44 718677.969
96 3624.579 2919.86153 6544.44 715068.130
97 3639.379 2905.06117 6544.44 711443.551
98 3654.240 2890.20037 6544.44 707804.172
99 3669.162 2875.27889 6544.44 704149.932
100 3684.144 2860.29648 6544.44 700480.770
101 3699.188 2845.25289 6544.44 696796.626
102 3714.293 2830.14788 6544.44 693097.439
103 3729.459 2814.98118 6544.44 689383.146
104 3744.688 2799.75255 6544.44 685653.687
105 3759.979 2784.46175 6544.44 681908.999
106 3775.332 2769.10850 6544.44 678149.020
107 3790.748 2753.69256 6544.44 674373.688
108 3806.227 2738.21367 6544.44 670582.940
109 3821.769 2722.67158 6544.44 666776.713
110 3837.374 2707.06602 6544.44 662954.945
111 3853.044 2691.39674 6544.44 659117.570
112 3868.777 2675.66348 6544.44 655264.526
113 3884.575 2659.86598 6544.44 651395.749
114 3900.437 2644.00396 6544.44 647511.175
115 3916.363 2628.07718 6544.44 643610.738
116 3932.355 2612.08536 6544.44 639694.375
117 3948.412 2596.02825 6544.44 635762.020
118 3964.535 2579.90556 6544.44 631813.608
119 3980.723 2563.71705 6544.44 627849.073
120 3996.978 2547.46243 6544.44 623868.349
121 4013.299 2531.14143 6544.44 619871.371
122 4029.687 2514.75379 6544.44 615858.072
123 4046.141 2498.29924 6544.44 611828.385
124 4062.663 2481.77750 6544.44 607782.244
125 4079.252 2465.18829 6544.44 603719.581
126 4095.909 2448.53134 6544.44 599640.329
127 4112.634 2431.80638 6544.44 595544.420
128 4129.427 2415.01313 6544.44 591431.786
129 4146.289 2398.15130 6544.44 587302.358
130 4163.220 2381.22062 6544.44 583156.069
131 4180.220 2364.22080 6544.44 578992.849
132 4197.289 2347.15157 6544.44 574812.630
133 4214.428 2330.01264 6544.44 570615.341
134 4231.637 2312.80373 6544.44 566400.913
135 4248.916 2295.52454 6544.44 562169.276
136 4266.266 2278.17480 6544.44 557920.360
137 4283.686 2260.75422 6544.44 553654.094
138 4301.178 2243.26250 6544.44 549370.408
139 4318.741 2225.69936 6544.44 545069.230
140 4336.376 2208.06450 6544.44 540750.489
141 4354.083 2190.35763 6544.44 536414.113
142 4371.862 2172.57846 6544.44 532060.030
143 4389.714 2154.72669 6544.44 527688.168
144 4407.638 2136.80202 6544.44 523298.454
145 4425.636 2118.80416 6544.44 518890.816
146 4443.708 2100.73282 6544.44 514465.180
147 4461.853 2082.58768 6544.44 510021.472
148 4480.072 2064.36844 6544.44 505559.619
149 4498.366 2046.07482 6544.44 501079.547
150 4516.734 2027.70649 6544.44 496581.181
151 4535.177 2009.26316 6544.44 492064.447
152 4553.696 1990.74452 6544.44 487529.270
153 4572.290 1972.15026 6544.44 482975.574
154 4590.960 1953.48008 6544.44 478403.284
155 4609.707 1934.73365 6544.44 473812.323
156 4628.530 1915.91068 6544.44 469202.617
157 4647.430 1897.01085 6544.44 464574.087
158 4666.407 1878.03385 6544.44 459926.657
159 4685.461 1858.97936 6544.44 455260.251
160 4704.593 1839.84706 6544.44 450574.789
161 4723.804 1820.63663 6544.44 445870.196
162 4743.093 1801.34777 6544.44 441146.392
163 4762.460 1781.98014 6544.44 436403.299
164 4781.907 1762.53343 6544.44 431640.839
165 4801.433 1743.00731 6544.44 426858.932
166 4821.039 1723.40145 6544.44 422057.499
167 4840.725 1703.71554 6544.44 417236.460
168 4860.491 1683.94925 6544.44 412395.735
169 4880.338 1664.10224 6544.44 407535.244
170 4900.266 1644.17420 6544.44 402654.905
171 4920.276 1624.16478 6544.44 397754.639
172 4940.367 1604.07365 6544.44 392834.363
173 4960.540 1583.90049 6544.44 387893.996
174 4980.796 1563.64495 6544.44 382933.456
175 5001.134 1543.30670 6544.44 377952.661
176 5021.555 1522.88540 6544.44 372951.527
177 5042.060 1502.38072 6544.44 367929.972
178 5062.648 1481.79231 6544.44 362887.912
179 5083.321 1461.11983 6544.44 357825.264
180 5104.078 1440.36294 6544.44 352741.943
181 5124.919 1419.52129 6544.44 347637.866
182 5145.846 1398.59453 6544.44 342512.947
183 5166.858 1377.58233 6544.44 337367.101
184 5187.956 1356.48432 6544.44 332200.243
185 5209.140 1335.30017 6544.44 327012.286
186 5230.411 1314.02951 6544.44 321803.146
187 5251.768 1292.67200 6544.44 316572.735
188 5273.213 1271.22728 6544.44 311320.967
189 5294.745 1249.69499 6544.44 306047.753
190 5316.366 1228.07478 6544.44 300753.008
191 5338.074 1206.36629 6544.44 295436.642
192 5359.871 1184.56915 6544.44 290098.568
193 5381.757 1162.68301 6544.44 284738.697
194 5403.733 1140.70750 6544.44 279356.939
195 5425.798 1118.64226 6544.44 273953.206
196 5447.954 1096.48692 6544.44 268527.408
197 5470.199 1074.24111 6544.44 263079.454
198 5492.536 1051.90446 6544.44 257609.255
199 5514.964 1029.47660 6544.44 252116.719
200 5537.483 1006.95717 6544.44 246601.755
201 5560.095 984.34578 6544.44 241064.272
202 5582.798 961.64206 6544.44 235504.177
203 5605.595 938.84563 6544.44 229921.379
204 5628.484 915.95612 6544.44 224315.784
205 5651.467 892.97314 6544.44 218687.299
206 5674.544 869.89631 6544.44 213035.832
207 5697.715 846.72526 6544.44 207361.288
208 5720.981 823.45959 6544.44 201663.573
209 5744.342 800.09892 6544.44 195942.592
210 5767.798 776.64285 6544.44 190198.250
211 5791.349 753.09101 6544.44 184430.452
212 5814.997 729.44300 6544.44 178639.103
213 5838.742 705.69843 6544.44 172824.106
214 5862.584 681.85690 6544.44 166985.363
215 5886.522 657.91802 6544.44 161122.780
216 5910.559 633.88138 6544.44 155236.257
217 5934.694 609.74660 6544.44 149325.698
218 5958.927 585.51327 6544.44 143391.004
219 5983.260 561.18098 6544.44 137432.077
220 6007.691 536.74934 6544.44 131448.818
221 6032.223 512.21793 6544.44 125441.127
222 6056.854 487.58636 6544.44 119408.904
223 6081.586 462.85420 6544.44 113352.050
224 6106.419 438.02106 6544.44 107270.464
225 6131.354 413.08651 6544.44 101164.044
226 6156.390 388.05015 6544.44 95032.690
227 6181.529 362.91156 6544.44 88876.300
228 6206.770 337.67031 6544.44 82694.771
229 6232.114 312.32600 6544.44 76488.001
230 6257.562 286.87820 6544.44 70255.886
231 6283.114 261.32649 6544.44 63998.324
232 6308.770 235.67044 6544.44 57715.210
233 6334.531 209.90963 6544.44 51406.440
234 6360.397 184.04363 6544.44 45071.909
235 6386.368 158.07201 6544.44 38711.512
236 6412.446 131.99434 6544.44 32325.144
237 6438.630 105.81018 6544.44 25912.698
238 6464.921 79.51911 6544.44 19474.067
239 6491.320 53.12068 6544.44 13009.146
240 6517.826 26.61446 6544.44 6517.826
>忘记计算利息差额：
添加入下：
完整代码：
#输入数据
B <- 1000000
R <- 0.049/12 #月利率
t <- 20*12 #分t期还款
N <- c(1:t)
one <- data.frame('等额本金每月偿还本金'=0,'等额本金每月偿还利息'=0,'等额本金每月偿还本息和'=0,'等额本金每月剩余本金'=0)
one
#等额本金
a=0#计算利息总和
MBA <- B/t #每月偿还本金=贷款总额/贷款月数
for(i in N){
MYA <- B - MBA*(i-1) #每月剩余本金
MIA <- MYA*R #每月偿还利息=剩余本金*月利率
a=a+MIA
MPA <- MIA + MBA #每月偿还本息和
one[i,] <- data.frame('等额本金每月偿还本金'=MBA,'等额本金每月偿还利息'=MIA,'等额本金每月偿还本息和'=MPA,'等额本金每月剩余本金'=MYA)
}
one
a
# 等额本息
MPB <- B*R*(1+R)^t / ((1+R)^t-1) # 每月应还的等额本息，包含月还利息和月还本金
two <- data.frame('等额本息每月偿还本金'=0,'等额本息每月偿还利息'=0,'等额本息每月偿还本息和'=0,'等额本息每月剩余本金'=0)
two
MYBF <- function(n) # 如何将利息与本金分离出来
{
# 可知，MYB(n)为第n个月后剩余的欠银行的钱,即第n个月的剩余本金(n=1,2,3..)
# 那么MYB(N),N=0,1,2,...,且MYB(N)*r就是第N+1个月的利息
MYB <- B*(1+R)^n - MPB*((1+R)^n-1)/R
return(MYB)
}
b=0#计算利息总和
for(i in N-1){
MYB <- MYBF(i) # 让时间从0,1,2,3...到n-1结束 #每月剩余本金
MIB <- MYB * R # 月还利息
b=b+MIB
MBB <- MPB - MIB # 月还本金
two[i+1,] <- data.frame('等额本息每月偿还本金'=MBB,'等额本息每月偿还利息'=MIB,'等额本息每月偿还本息和'=MPB,'等额本金每月剩余本金'=MYB)
}
two
b
#等额本息偿还利息总和-等额本金偿还利息总和
c=b-a
print("等额本息偿还利息总和-等额本金偿还利息总和")
c等额本息偿还利息总和-等额本金偿还利息总和-----运行结果
> a
[1] 492041.7
> b
[1] 570665.7
> #等额本息偿还利息总和-等额本金偿还利息总和
> c=b-a
> print("等额本息偿还利息总和-等额本金偿还利息总和")
[1] "等额本息偿还利息总和-等额本金偿还利息总和"
> c
[1] 78624.05
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