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數學公式

數學公式: 貸款還款計劃試算器
Show calculation steps (1)
  1. Equal principal

    Equal principal: 貸款還款計劃試算器

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

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結果

每期還款額
92,013
over 120 payments
貸款金額(原幣值) 10,000,000
首期還款 92,013
末期還款 94,371.34
還款總額 11,180,503.34
累計利息 1,180,503.34
# 還款額 利息 本金 剩餘本金
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

這個試算器能幫你做什麼

「貸款還款計劃試算器」會算出你每期應繳的金額,並產生一份完整的攤還明細表,逐期列出利息、本金與剩餘本金。它支援兩種常見的還款方式,可設定貸款期間中途調整利率,也能設定只繳利息的寬限期。背後採用標準的攤還公式,適用於任何幣別。

使用方式

先輸入貸款金額(可選擇一般幣值單位,或以「萬」為單位的 x10,000),接著選擇還款方式、還款頻率與進位規則,再填入利率與貸款年期。若是固定利率貸款,只要把「之後利率」設為與初始利率相同即可。如果你只想看期數而不需要對應的日曆日期,將起始年份留空即可。

公式說明

採用本息平均攤還(每期還款總額相同)時,每個固定利率階段使用 $$A = \frac{B \cdot i}{1 - (1 + i)^{-n}}$$,其中 \(B\) 為目前的剩餘本金,\(i\) 為每期利率(年利率 / 100 / 每年還款次數),\(n\) 為剩餘還款期數。每一期的利息等於 \(B \cdot i\),其餘金額則用來償還本金。若採用本金平均攤還,每期償還的本金固定為 \(P/n\),利息則逐期遞減,因此每期還款總額會隨時間下降。最後一期會略作調整以吸收進位誤差,讓剩餘本金正好歸零。

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堆疊長條圖顯示等額還款隨時間分解為遞減的利息與遞增的本金
本息平均攤還每期還款額相同,其中利息逐漸減少、本金償還逐漸增加。

實例試算

假設借款 10,000,000,固定年利率 2%、期間 10 年、每月還款。每期利率 \(i = 0.02/12 = 0.00166667\),總期數 \(N = 120\)。每月還款額 $$A = \frac{10{,}000{,}000 \times 0.00166667}{1 - 1.00166667^{-120}} \approx 92{,}013$$ 還款總額約 11,041,560,因此累計利息約為 1,041,560。

折線圖比較固定的本息平均攤還與遞減的本金平均攤還
本息平均攤還保持不變;本金平均攤還初期較高,並在還款期內逐漸下降。

常見問題

為什麼最後一期的金額不一樣?每期還款金額經過進位後會留下些微誤差,這個尾差會由最後一期一併吸收,使剩餘本金歸零。

什麼是寬限期?在寬限期內只需繳交利息;寬限期結束後才開始償還本金,並以剩餘期數進行攤還。

計算結果跟我的銀行一致嗎?本結果僅供參考。各家銀行採用的進位方式與計息天數規則不同,實際還款明細可能略有差異。

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