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数学公式

数学公式: 贷款还款计划计算器
Show calculation steps (1)
  1. Equal principal

    Equal principal: 贷款还款计划计算器

    Constant principal portion plus declining interest on the current balance B.

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结果

每期还款额
92,013
over 120 payments
贷款金额(基础货币) 10,000,000
首期还款 92,013
末期还款 94,371.34
累计还款总额 11,180,503.34
累计利息总额 1,180,503.34
# 还款额 利息 本金 剩余余额
1 92,013 16,666.67 75,346.33 9,924,653.67
2 92,013 16,541.09 75,471.91 9,849,181.76
3 92,013 16,415.3 75,597.7 9,773,584.06
4 92,013 16,289.31 75,723.69 9,697,860.37
5 92,013 16,163.1 75,849.9 9,622,010.47
6 92,013 16,036.68 75,976.32 9,546,034.15
7 92,013 15,910.06 76,102.94 9,469,931.21
8 92,013 15,783.22 76,229.78 9,393,701.43
9 92,013 15,656.17 76,356.83 9,317,344.6
10 92,013 15,528.91 76,484.09 9,240,860.5
11 92,013 15,401.43 76,611.57 9,164,248.94
12 92,013 15,273.75 76,739.25 9,087,509.69
13 92,013 15,145.85 76,867.15 9,010,642.53
14 92,013 15,017.74 76,995.26 8,933,647.27
15 92,013 14,889.41 77,123.59 8,856,523.68
16 92,013 14,760.87 77,252.13 8,779,271.56
17 92,013 14,632.12 77,380.88 8,701,890.68
18 92,013 14,503.15 77,509.85 8,624,380.83
19 92,013 14,373.97 77,639.03 8,546,741.8
20 92,013 14,244.57 77,768.43 8,468,973.37
21 92,013 14,114.96 77,898.04 8,391,075.32
22 92,013 13,985.13 78,027.87 8,313,047.45
23 92,013 13,855.08 78,157.92 8,234,889.53
24 92,013 13,724.82 78,288.18 8,156,601.34
25 92,013 13,594.34 78,418.66 8,078,182.68
26 92,013 13,463.64 78,549.36 7,999,633.31
27 92,013 13,332.72 78,680.28 7,920,953.04
28 92,013 13,201.59 78,811.41 7,842,141.63
29 92,013 13,070.24 78,942.76 7,763,198.86
30 92,013 12,938.66 79,074.34 7,684,124.53
31 92,013 12,806.87 79,206.13 7,604,918.4
32 92,013 12,674.86 79,338.14 7,525,580.26
33 92,013 12,542.63 79,470.37 7,446,109.9
34 92,013 12,410.18 79,602.82 7,366,507.08
35 92,013 12,277.51 79,735.49 7,286,771.59
36 92,013 12,144.62 79,868.38 7,206,903.21
37 92,013 12,011.51 80,001.49 7,126,901.72
38 92,013 11,878.17 80,134.83 7,046,766.89
39 92,013 11,744.61 80,268.39 6,966,498.5
40 92,013 11,610.83 80,402.17 6,886,096.33
41 92,013 11,476.83 80,536.17 6,805,560.16
42 92,013 11,342.6 80,670.4 6,724,889.76
43 92,013 11,208.15 80,804.85 6,644,084.91
44 92,013 11,073.47 80,939.53 6,563,145.38
45 92,013 10,938.58 81,074.42 6,482,070.96
46 92,013 10,803.45 81,209.55 6,400,861.41
47 92,013 10,668.1 81,344.9 6,319,516.51
48 92,013 10,532.53 81,480.47 6,238,036.04
49 92,013 10,396.73 81,616.27 6,156,419.77
50 92,013 10,260.7 81,752.3 6,074,667.46
51 92,013 10,124.45 81,888.55 5,992,778.91
52 92,013 9,987.96 82,025.04 5,910,753.88
53 92,013 9,851.26 82,161.74 5,828,592.13
54 92,013 9,714.32 82,298.68 5,746,293.45
55 92,013 9,577.16 82,435.84 5,663,857.61
56 92,013 9,439.76 82,573.24 5,581,284.37
57 92,013 9,302.14 82,710.86 5,498,573.51
58 92,013 9,164.29 82,848.71 5,415,724.8
59 92,013 9,026.21 82,986.79 5,332,738.01
60 92,013 8,887.9 83,125.1 5,249,612.91
61 94,328 13,124.03 81,203.97 5,168,408.94
62 94,328 12,921.02 81,406.98 5,087,001.96
63 94,328 12,717.5 81,610.5 5,005,391.46
64 94,328 12,513.48 81,814.52 4,923,576.94
65 94,328 12,308.94 82,019.06 4,841,557.89
66 94,328 12,103.89 82,224.11 4,759,333.78
67 94,328 11,898.33 82,429.67 4,676,904.11
68 94,328 11,692.26 82,635.74 4,594,268.38
69 94,328 11,485.67 82,842.33 4,511,426.05
70 94,328 11,278.57 83,049.43 4,428,376.61
71 94,328 11,070.94 83,257.06 4,345,119.55
72 94,328 10,862.8 83,465.2 4,261,654.35
73 94,328 10,654.14 83,673.86 4,177,980.49
74 94,328 10,444.95 83,883.05 4,094,097.44
75 94,328 10,235.24 84,092.76 4,010,004.68
76 94,328 10,025.01 84,302.99 3,925,701.69
77 94,328 9,814.25 84,513.75 3,841,187.95
78 94,328 9,602.97 84,725.03 3,756,462.92
79 94,328 9,391.16 84,936.84 3,671,526.08
80 94,328 9,178.82 85,149.18 3,586,376.89
81 94,328 8,965.94 85,362.06 3,501,014.83
82 94,328 8,752.54 85,575.46 3,415,439.37
83 94,328 8,538.6 85,789.4 3,329,649.97
84 94,328 8,324.12 86,003.88 3,243,646.09
85 94,328 8,109.12 86,218.88 3,157,427.21
86 94,328 7,893.57 86,434.43 3,070,992.78
87 94,328 7,677.48 86,650.52 2,984,342.26
88 94,328 7,460.86 86,867.14 2,897,475.11
89 94,328 7,243.69 87,084.31 2,810,390.8
90 94,328 7,025.98 87,302.02 2,723,088.78
91 94,328 6,807.72 87,520.28 2,635,568.5
92 94,328 6,588.92 87,739.08 2,547,829.42
93 94,328 6,369.57 87,958.43 2,459,871
94 94,328 6,149.68 88,178.32 2,371,692.67
95 94,328 5,929.23 88,398.77 2,283,293.9
96 94,328 5,708.23 88,619.77 2,194,674.14
97 94,328 5,486.69 88,841.31 2,105,832.82
98 94,328 5,264.58 89,063.42 2,016,769.41
99 94,328 5,041.92 89,286.08 1,927,483.33
100 94,328 4,818.71 89,509.29 1,837,974.04
101 94,328 4,594.94 89,733.06 1,748,240.97
102 94,328 4,370.6 89,957.4 1,658,283.58
103 94,328 4,145.71 90,182.29 1,568,101.29
104 94,328 3,920.25 90,407.75 1,477,693.54
105 94,328 3,694.23 90,633.77 1,387,059.77
106 94,328 3,467.65 90,860.35 1,296,199.42
107 94,328 3,240.5 91,087.5 1,205,111.92
108 94,328 3,012.78 91,315.22 1,113,796.7
109 94,328 2,784.49 91,543.51 1,022,253.19
110 94,328 2,555.63 91,772.37 930,480.82
111 94,328 2,326.2 92,001.8 838,479.03
112 94,328 2,096.2 92,231.8 746,247.22
113 94,328 1,865.62 92,462.38 653,784.84
114 94,328 1,634.46 92,693.54 561,091.3
115 94,328 1,402.73 92,925.27 468,166.03
116 94,328 1,170.42 93,157.58 375,008.45
117 94,328 937.52 93,390.48 281,617.97
118 94,328 704.04 93,623.96 187,994.01
119 94,328 469.99 93,858.01 94,136
120 94,371.34 235.34 94,136 0

这个计算器能做什么

贷款还款计划计算器可以算出你每期需要偿还的金额,并生成一份完整的摊还明细表,清楚列出每一期还款中的利息部分、本金部分以及剩余本金余额。它支持两种常见的还款方式,可设置贷款中途的利率变动,也支持期初宽限期(递延期)——在宽限期内只需支付利息。其计算逻辑采用标准的摊还公式,适用于任何币种。

使用方法

输入贷款金额(可选择普通货币单位,或日本常用的「万円」即 x10,000 单位),选择还款方式、还款频率和取整规则,再填入利率和贷款期限。若为固定利率贷款,只需将「之后利率」设为与初始利率相同即可。如果你只想看期数而不需要具体日期,把起始年份留空即可。

计算公式说明

对于等额本息还款方式,每个固定利率阶段都采用 $$A = \frac{B \cdot i}{1 - (1 + i)^{-n}}$$ 计算,其中 \(B\) 为当前本金余额,\(i\) 为每期利率(年利率 / 100 / 每年还款期数),\(n\) 为剩余还款期数。每期的利息等于 \(B \cdot i\),其余部分用于偿还本金。对于等额本金还款方式,每期偿还的本金固定为 \(P/n\),而利息随余额减少逐期下降,因此每期还款总额会越来越少。最后一期会进行微调,以消除取整产生的尾差,确保余额恰好归零。

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堆叠柱状图显示等额还款随时间分解为递减的利息和递增的本金
等额本息还款每期还款额相同,其中利息逐渐减少、本金偿还逐渐增加。

实例演算

假设借款 10,000,000,固定年利率 2%,期限 10 年,按月还款。每期利率 \(i = 0.02/12 = 0.00166667\),总期数 \(N = 120\)。每月还款额 $$A = \frac{10{,}000{,}000 \times 0.00166667}{1 - 1.00166667^{-120}} \approx 92{,}013$$ 累计还款总额约为 11,041,560,因此总利息约为 1,041,560。

折线图比较固定的等额本息还款与递减的等额本金还款
等额本息还款保持不变;等额本金还款初期较高,并在还款期内逐渐下降。

常见问题

为什么最后一期的金额不一样?由于每期还款额都经过取整,会累积出一点小小的尾差,这部分差额由最后一期一并结清,使余额归零。

什么是宽限期?在宽限期内你只需偿还利息;本金的偿还从宽限期结束后开始,并在剩余期数内按摊还方式分摊。

这个结果和我的银行一致吗?计算结果仅供参考。各家银行在取整方式和计息天数惯例上有所不同,因此你实际的还款计划可能略有差异。

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