-----------------------------《PHP與MySQL程序設計(第四版)》中第73頁4.2.6節分期還貸計算器數學原理分析。
《PHP與MySQL程序設計(第四版)》中73頁4.2.6節，代碼清單4-1是還貸計算器函數amortizationTable，代碼如下。
其使用的是等額本息分期還款模型。要理解這段代碼，關鍵是理解月還款額b的計算公式背後的數學原理。
設本金a，還款月數n，月利率r,每月還款b。還款計算如下：
首月利息a*r,還款後，餘額a1=a(1+r)-b;次月利息a1*r,次月還款後餘額a2=a1(1+r)-b=(a(1+r)-b)(1+r)-b=a(1+r)^2-b[(1+r)+1],
如此類推，最後一個月還清，有餘額an=a(1+r)^n-b[(1+r)^(n-1)+(1+r)^(n-2)+……1]=0。
可見中括號內爲等比數列，根據等比數列計算公式可得an=a(1+r)^n-b((1+r)^n-1)/r = 0,所以有b=ar(1+r)^n/((1+r)^n-1)。
代碼中，$periodicPayment即b,$balance即a,$intCalc即1+r，$totalPayments即n，所以有
$periodicPayment = $balance * pow($intCalc,$totalPayments) * ($intCalc - 1) /
(pow($intCalc,$totalPayments) - 1);
回過頭再看計算器函數，根據以上原理分析，每月的計算如下：
設上期貸款餘額a1，本期餘額a2,則有：a2=a1(1+r)-b=a1-(b-a1×r)，也就是本期還款剔除利息，剩餘的就是上期餘額扣除部分，
得到本期餘額，如此迭代。體現在代碼上就是：
$paymentInterest = round($balance * $monthlyInterest, 2);
$paymentPrincipal = round($periodicPayment - $paymentInterest, 2);
$newBalance = round($balance - $paymentPrincipal, 2);
////////////////分期還貸計算器完整代碼
<?php
function amortizationTable($pNum, $periodicPayment, $balance, $monthlyInterest)
{
// Calculate payment interest
$paymentInterest = round($balance * $monthlyInterest, 2);
// Calculate payment principal
$paymentPrincipal = round($periodicPayment - $paymentInterest, 2);
// Deduct principal from remaining balance
$newBalance = round($balance - $paymentPrincipal, 2);
// If new balance < monthly payment, set to zero
if ($newBalance < $paymentPrincipal) {
$newBalance = 0;
}
printf("<tr><td>%d</td>", $pNum);
printf("<td>$%s</td>", number_format($newBalance, 2));
printf("<td>$%s</td>", number_format($periodicPayment, 2));
printf("<td>$%s</td>", number_format($paymentPrincipal, 2));
printf("<td>$%s</td></tr>", number_format($paymentInterest, 2));
# If balance not yet zero, recursively call amortizationTable()
if ($newBalance > 0) {
$pNum++;
amortizationTable($pNum, $periodicPayment,
$newBalance, $monthlyInterest);
} else {
return 0;
}
}
// Loan balance
$balance = 10000.00;
// Loan interest rate
$interestRate = .0575;
// Monthly interest rate
$monthlyInterest = $interestRate / 12;
// Term length of the loan, in years.
$termLength = 5;
// Number of payments per year.
$paymentsPerYear = 12;
// Payment iteration
$paymentNumber = 1;
//還款月數m
// Determine total number payments
$totalPayments = $termLength * $paymentsPerYear;
//複利1+r
// Determine interest component of periodic payment
$intCalc = 1 + $interestRate / $paymentsPerYear;
//計算月還款額b
// Determine periodic payment
$periodicPayment = $balance * pow($intCalc,$totalPayments) * ($intCalc - 1) /
(pow($intCalc,$totalPayments) - 1);
// Round periodic payment to two decimals
$periodicPayment = round($periodicPayment,2);
// Create table
echo "<table width='50%' align='center' border='1'>";
echo "<tr>
<th>Payment Number</th><th>Balance</th>
<th>Payment</th><th>Principal</th><th>Interest</th>
</tr>";
// Call recursive function
amortizationTable($paymentNumber, $periodicPayment, $balance,
$monthlyInterest);
// Close table
echo "</table>";
?>
//////////以上代碼貸款1萬元5年還清，年息（5.75%）,代碼運行結果得出的還款逐月情況如下：
Payment Number Balance Payment Principal Interest
1 $9,855.75 $192.17 $144.25 $47.92
2 $9,710.81 $192.17 $144.94 $47.23
3 $9,565.17 $192.17 $145.64 $46.53
4 $9,418.83 $192.17 $146.34 $45.83
5 $9,271.79 $192.17 $147.04 $45.13
6 $9,124.05 $192.17 $147.74 $44.43
7 $8,975.60 $192.17 $148.45 $43.72
8 $8,826.44 $192.17 $149.16 $43.01
9 $8,676.56 $192.17 $149.88 $42.29
10 $8,525.97 $192.17 $150.59 $41.58
11 $8,374.65 $192.17 $151.32 $40.85
12 $8,222.61 $192.17 $152.04 $40.13
13 $8,069.84 $192.17 $152.77 $39.40
14 $7,916.34 $192.17 $153.50 $38.67
15 $7,762.10 $192.17 $154.24 $37.93
16 $7,607.12 $192.17 $154.98 $37.19
17 $7,451.40 $192.17 $155.72 $36.45
18 $7,294.93 $192.17 $156.47 $35.70
19 $7,137.71 $192.17 $157.22 $34.95
20 $6,979.74 $192.17 $157.97 $34.20
21 $6,821.01 $192.17 $158.73 $33.44
22 $6,661.52 $192.17 $159.49 $32.68
23 $6,501.27 $192.17 $160.25 $31.92
24 $6,340.25 $192.17 $161.02 $31.15
25 $6,178.46 $192.17 $161.79 $30.38
26 $6,015.90 $192.17 $162.56 $29.61
27 $5,852.56 $192.17 $163.34 $28.83
28 $5,688.43 $192.17 $164.13 $28.04
29 $5,523.52 $192.17 $164.91 $27.26
30 $5,357.82 $192.17 $165.70 $26.47
31 $5,191.32 $192.17 $166.50 $25.67
32 $5,024.03 $192.17 $167.29 $24.88
33 $4,855.93 $192.17 $168.10 $24.07
34 $4,687.03 $192.17 $168.90 $23.27
35 $4,517.32 $192.17 $169.71 $22.46
36 $4,346.80 $192.17 $170.52 $21.65
37 $4,175.46 $192.17 $171.34 $20.83
38 $4,003.30 $192.17 $172.16 $20.01
39 $3,830.31 $192.17 $172.99 $19.18
40 $3,656.49 $192.17 $173.82 $18.35
41 $3,481.84 $192.17 $174.65 $17.52
42 $3,306.35 $192.17 $175.49 $16.68
43 $3,130.02 $192.17 $176.33 $15.84
44 $2,952.85 $192.17 $177.17 $15.00
45 $2,774.83 $192.17 $178.02 $14.15
46 $2,595.96 $192.17 $178.87 $13.30
47 $2,416.23 $192.17 $179.73 $12.44
48 $2,235.64 $192.17 $180.59 $11.58
49 $2,054.18 $192.17 $181.46 $10.71
50 $1,871.85 $192.17 $182.33 $9.84
51 $1,688.65 $192.17 $183.20 $8.97
52 $1,504.57 $192.17 $184.08 $8.09
53 $1,319.61 $192.17 $184.96 $7.21
54 $1,133.76 $192.17 $185.85 $6.32
55 $947.02 $192.17 $186.74 $5.43
56 $759.39 $192.17 $187.63 $4.54
57 $570.86 $192.17 $188.53 $3.64
58 $381.43 $192.17 $189.43 $2.74
59 $191.09 $192.17 $190.34 $1.83
60 $0.00 $192.17 $191.25 $0.92