The decreasing loan calculation

  • Created:
  • / Author: Aaron Lewis
The 15 year loan of 100000 yuan, according to the loan period, the benchmark interest rate 7.83% matching principal (monthly decline) calculation:
Monthly principal: 100000 / 180 months = 555.56 yuan
The first month should also interest: 100000 * 0.6525% = 652.5 yuan monthly interest rate
The first month of the amount for the month: 555.56 + 652.5 = 1208.06 yuan
Second months of interest: the remaining principal 99444.44 × month rate of 0.6525% = 648.87
Second months of the amount for the month: 555.56 + 648.87 = 1204.43 yuan
And so on.
. SimilarlyA matching principal)
1On Principal= the loan principal / total repayment months(Note: monthly principal is fixed data)
2 this month owing on the loan, this month also owes the bank loan principal (abbreviated as at the end of outstanding principal), i.e.:
　　Article n the end of the outstanding principalThe principal of the loan principal = -n* = loan principal * (1-N / total repayment months)
3The interest of this monthAt the end of the outstanding principal * = monthly interest rate, i.e.:
The N monthly interest = a (n-1) at the end of the outstanding principal * monthly interest rate = loan principal *[1- (n-1) / total repayment months hard on interest rates
4The monthly repayment= on principal + interest this month, i.e.:
Article n the repayment of the loan principal repayment = / total number of months + loan principal *[1- (n-1) / total repayment months hard on interest rates
5 of the total interest = first months of interest plus second months of interest + third months of interest +... + the total repayment months interest = total loan number * monthly interest rate *[1+1+... +1- (0+1+2+... + total repayment months -1) / total repayment months], of which, 1+2+ + total repayment months... -1, is the arithmetic progression, similar to trapezoid formula, and = (on the bottom and bottom) * /2, therefore,
　　Total interest loan principal * * = monthly interest rate (the total repayment months +1) / 2
2,Matching principalRepayment law, the monthly repayment of the loan principal, interest on loans with principal month after month, monthly repayment amount (the + message) gradually reduce. Total interest payments is less than the matching service law. Suitable for high income and some savings middle-aged people. Formula for the:
The monthly repayment amount = loan principal / total repayment months + (the loan principal repayment of principal - accumulated) * monthly interest
Among them:Total loan principal repayment of principal = / total repayment months * have repayment months
In the above formula, have repayment months is changing, so the monthly repayment amount is changing, we put the formula to transform it becomes:
The monthly repayment amount =The loan principal / total repayment months+ (The principal of the loan interest rate * month-The loan principal / total alsoMonthly number * monthly interest* have repayment months)
Among them:The loan principal / total repayment months, we call itMonthly principal, is a fixed value;The principal of the loan interest rate * month, we call itThe first month of interest payable, is a fixed value;The loan principal /The total repayment months * monthly interest rate = monthly principal * monthly interest, we call itSpreads, is a fixed value; the first month of interest payable - spread * have repayment months, is the month to also interest, it is a variable that is:ArticleX month interest payable = first month interest payable - spread * (X-1);The total interest payable= all months monthly interest payable sum, is that you spending all interest.
 
15 years 420000 yuan of loans, loan period, according to the lower limit of the annual interest rate of 6.35% matching principal (monthly decline) calculation:
Monthly principal: 420000 / 180 months = 2333.3 yuan
The first month should also interest: 420000 * 0.529125% = 2222.3 yuan monthly interest rate  
The first month of the amount for the month 2333.3 yuan +2222.3 yuan =4555.6 yuan
Second months should also interest 417666.7 x monthly interest rate 0.529125%=2210
Second months of the amount for the month  2333.3 yuan +2210 yuan =4543.3
In January, 4555.83 (yuan)
In February, 4543.49 (yuan)
In March, 4531.14 (yuan)
In April, 4518.79 (yuan)
In May, 4506.44 (yuan)
In June, 4494.1 (yuan)
In July, 4481.75 (yuan)
In August, 4469.4 (yuan)
In September, 4457.06 (yuan)
In October, 4444.71 (yuan)
In November, 4432.36 (yuan)
In December, 4420.01 (yuan)
13 months, 4407.67 (yuan)
14 months, 4395.32 (yuan)
15 months, 4382.97 (yuan)
16 months, 4370.63 (yuan)
17 months, 4358.28 (yuan)
18 months, 4345.93 (yuan)
19 months, 4333.58 (yuan)
20 months, 4321.24 (yuan)
21 months, 4308.89 (yuan)
22 months, 4296.54 (yuan)
23 months, 4284.19 (yuan)
24 months, 4271.85 (yuan)
25 months, 4259.5 (yuan)
26 months, 4247.15 (yuan)
27 months, 4234.81 (yuan)
28 months, 4222.46 (yuan)
29 months, 4210.11 (yuan)
30 months, 4197.76 (yuan)
31 months, 4185.42 (yuan)
32 months, 4173.07 (yuan)
33 months, 4160.72 (yuan)
34 months, 4148.38 (yuan)
35 months, 4136.03 (yuan)
36 months, 4123.68 (yuan)
37 months, 4111.33 (yuan)
38 months, 4098.99 (yuan)
39 months, 4086.64 (yuan)
40 months, 4074.29 (yuan)
41 months, 4061.94 (yuan)
42 months, 4049.6 (yuan)
43 months, 4037.25 (yuan)
44 months, 4024.9 (yuan)
45 months, 4012.56 (yuan)
46 months, 4000.21 (yuan)
47 months, 3987.86 (yuan)
48 months, 3975.51 (yuan)
49 months, 3963.17 (yuan)
50 months, 3950.82 (yuan)
51 months, 3938.47 (yuan)
52 months, 3926.13 (yuan)
53 months, 3913.78 (yuan)
54 months, 3901.43 (yuan)
55 months, 3889.08 (yuan)
56 months, 3876.74 (yuan)
57 months, 3864.39 (yuan)
58 months, 3852.04 (yuan)
59 months, 3839.69 (yuan)
60 months, 3827.35 (yuan)
61 months, 3815 (yuan)
62 months, 3802.65 (yuan)
63 months, 3790.31 (yuan)
64 months, 3777.96 (yuan)
65 months, 3765.61 (yuan)
66 months, 3753.26 (yuan)
67 months, 3740.92 (yuan)
68 months, 3728.57 (yuan)
69 months, 3716.22 (yuan)
70 months, 3703.88 (yuan)
71 months, 3691.53 (yuan)
72 months, 3679.18 (yuan)
73 months, 3666.83 (yuan)
74 months, 3654.49 (yuan)
75 months, 3642.14 (yuan)
76 months, 3629.79 (yuan)
77 months, 3617.44 (yuan)
78 months, 3605.1 (yuan)
79 months, 3592.75 (yuan)
80 months, 3580.4 (yuan)
81 months, 3568.06 (yuan)
82 months, 3555.71 (yuan)
83 months, 3543.36 (yuan)
84 months, 3531.01 (yuan)
85 months, 3518.67 (yuan)
86 months, 3506.32 (yuan)
87 months, 3493.97 (yuan)
88 months, 3481.63 (yuan)
89 months, 3469.28 (yuan)
90 months, 3456.93 (yuan)
91 months, 3444.58 (yuan)
92 months, 3432.24 (yuan)
93 months, 3419.89 (yuan)
94 months, 3407.54 (yuan)
95 months, 3395.19 (yuan)
96 months, 3382.85 (yuan)
97 months, 3370.5 (yuan)
98 months, 3358.15 (yuan)
99 months, 3345.81 (yuan)
100 months, 3333.46 (yuan)
101 months, 3321.11 (yuan)
102 months, 3308.76 (yuan)
103 months, 3296.42 (yuan)
104 months, 3284.07 (yuan)
105 months, 3271.72 (yuan)
106 months, 3259.38 (yuan)
107 months, 3247.03 (yuan)
108 months, 3234.68 (yuan)
109 months, 3222.33 (yuan)
110 months, 3209.99 (yuan)
111 months, 3197.64 (yuan)
112 months, 3185.29 (yuan)
113 months, 3172.94 (yuan)
114 months, 3160.6 (yuan)
115 months, 3148.25 (yuan)
116 months, 3135.9 (yuan)
117 months, 3123.56 (yuan)
118 months, 3111.21 (yuan)
119 months, 3098.86 (yuan)
120 months, 3086.51 (yuan)
121 months, 3074.17 (yuan)
122 months, 3061.82 (yuan)
123 months, 3049.47 (yuan)
124 months, 3037.13 (yuan)
125 months, 3024.78 (yuan)
126 months, 3012.43 (yuan)
127 months, 3000.08 (yuan)
128 months, 2987.74 (yuan)
129 months, 2975.39 (yuan)
130 months, 2963.04 (yuan)
131 months, 2950.69 (yuan)
132 months, 2938.35 (yuan)
133 months, 2926 (yuan)
134 months, 2913.65 (yuan)
135 months, 2901.31 (yuan)
136 months, 2888.96 (yuan)
137 months, 2876.61 (yuan)
138 months, 2864.26 (yuan)
139 months, 2851.92 (yuan)
140 months, 2839.57 (yuan)
141 months, 2827.22 (yuan)
142 months, 2814.88 (yuan)
143 months, 2802.53 (yuan)
144 months, 2790.18 (yuan)
145 months, 2777.83 (yuan)
146 months, 2765.49 (yuan)
147 months, 2753.14 (yuan)
148 months, 2740.79 (yuan)
149 months, 2728.44 (yuan)
150 months, 2716.1 (yuan)
151 months, 2703.75 (yuan)
152 months, 2691.4 (yuan)
153 months, 2679.06 (yuan)
154 months, 2666.71 (yuan)
155 months, 2654.36 (yuan)
156 months, 2642.01 (yuan)
157 months, 2629.67 (yuan)
158 months, 2617.32 (yuan)
159 months, 2604.97 (yuan)
160 months, 2592.63 (yuan)
161 months, 2580.28 (yuan)
162 months, 2567.93 (yuan)
163 months, 2555.58 (yuan)
164 months, 2543.24 (yuan)
165 months, 2530.89 (yuan)
166 months, 2518.54 (yuan)
167 months, 2506.19 (yuan)
168 months, 2493.85 (yuan)
169 months, 2481.5 (yuan)
170 months, 2469.15 (yuan)
171 months, 2456.81 (yuan)
172 months, 2444.46 (yuan)
173 months, 2432.11 (yuan)
174 months, 2419.76 (yuan)
175 months, 2407.42 (yuan)
176 months, 2395.07 (yuan)
177 months, 2382.72 (yuan)
178 months, 2370.38 (yuan)
179 months, 2358.03 (yuan)
180 months, 2345.68 (yuan)