*4.21(计算不同利率下的贷款)编写程序，让用户输入贷款总额及以年为单位的贷款期限，以1/8为递增量，显示从5%到8%的利率下每月支付额和总偿还额。假设输入贷款总量为10 000，还贷期限为5年，所显示的输出如下:

贷款总额:to 000

年数:5

利率月支付额总偿还额

      5%188 .71   11322.74

      5 .125%189.28   11357.13

      5 .25%189.85   11391.59

...

//Exercise3_26.java: displays the monthly and total payments
//for each interest rate starting from 5% to 8%,
//with an incremental of 1/8.
import javax.swing.JOptionPane;
public class Exercise3_26 {
  // Main method
  public static void main(String[] args) {
    int numOfYears;
    double loanAmount;
    // Enter number of years
    String numOfYearsString = JOptionPane.showInputDialog(null,
      "Enter number of years as an integer, \nfor example 5:",
      "Exercise3_26 Input", JOptionPane.QUESTION_MESSAGE);
    // Convert string to int
    numOfYears = Integer.parseInt(numOfYearsString);
                                                                               
    // Enter loan amount
    String loanString = JOptionPane.showInputDialog(null,
      "Enter loan amount, for example 120000.95:",
      "Exercise3_26 Input", JOptionPane.QUESTION_MESSAGE);
    // Convert string to double
    loanAmount =  Double.parseDouble(loanString);
    // Display the header
    System.out.print("Interest Rate");
    System.out.print("\t" + "Monthly Payment");
    System.out.println("\t\t" + "Total Payment");
    double monthlyInterestRate;
    double monthlyPayment;
    double totalPayment;
    for (double annualInterestRate = 5.0; annualInterestRate <= 8.0;
      annualInterestRate += 1.0 / 8) {
      // Obtain monthly interest rate
      monthlyInterestRate = annualInterestRate / 1200;
      // Compute mortgage
      monthlyPayment = loanAmount*monthlyInterestRate/
        (1 - (Math.pow(1 / (1 + monthlyInterestRate), numOfYears * 12)));
      totalPayment = monthlyPayment * numOfYears * 12;
      // Display results
      System.out.print(annualInterestRate + "%");
      System.out.print("\t\t" + (int)(monthlyPayment * 100) / 100.0);
      System.out.println("\t\t\t" + (int)(totalPayment * 100) / 100.0);
    }
  }
}

**4.22(显示分期还贷时间表)对于给定的贷款额、月支付额包括偿还本金及利息。月利息是通过月利

率乘以余额(剩余本金)计算出来的。因此，每月偿还的本金等于月支付额减去月利息。编写一个程序，让用户输入贷款总额、贷款年数及利率，而后显示分期还贷时间表。假设输入的贷款总额为10 000，还贷期限为1年，年利率为7%，显示如下的表格:

贷款总额:10 000

年数:1

年利率:7%

月支付额:865.26

总偿还额：

10383.21

月份  利息  本金   余额

1     58.33 806.93 9193.07

2     53.62 811.64 8381.43

...

1 1   10.0  855.26 860.27

1 2   5.01  860.25 0.01

注:最后一次偿还后，余额可能不为0。如果是这样的话，最后一个月支付额应当是正常的月支付额加上最后的余额。

提示编写一个循环来打印该表。由于每个月的还贷额都是相同的，因此，应当在循环之前将其计算出来。开始时，余额即为贷款总额。在循环的每次迭代中，计算利息及本金，并更新余额。这个循环可以这样:

for (i =1;i <= numberOfYears * 12;i++) {

 interest = monthlyInterestRate * balance;

 principal = monthlyPayment - interest;

 balance = balance - principal;

 System.out.println(i + "\t\t" +interest

   + "\t\t" + principal +"\t\t" + balance);

}

import javax.swing.JOptionPane;
public class Exercise3_27 {
  public static void main(String[] args) {
    int numOfYears;
    double loanAmount;
                                   
    // Enter yearly interest rate
    String annualIntrestRateString = JOptionPane.showInputDialog(
      "Enter yearly interest rate, for example 8.25:");
    // Convert string to double
    double annualInterestRate =
      Double.parseDouble(annualIntrestRateString);
                                   
    // Obtain monthly interest rate
    double monthlyInterestRate = annualInterestRate/1200;
                                   
    // Enter number of years
    String numOfYearsString = JOptionPane.showInputDialog(
      "Enter number of years as an integer, \nfor example 5:");
    // Convert string to int
    numOfYears = Integer.parseInt(numOfYearsString);
                                   
    // Enter loan amount
    String loanString = JOptionPane.showInputDialog(
      "Enter loan amount, for example 120000.95:");
                                   
    // Convert string to double
    loanAmount =  Double.parseDouble(loanString);
                                   
    // Compute mortgage
    double monthlyPayment = loanAmount*monthlyInterestRate /
      (1 - (Math.pow(1 / (1 + monthlyInterestRate), numOfYears * 12)));
                                   
    double balance = loanAmount;
    double interest;
    double principal;
                                   
    System.out.println("Loan Amount: " + loanAmount);
    System.out.println("Number of Years: " + numOfYears);
    System.out.println("Interest Rate: " + annualInterestRate + "%");
    System.out.println();
    System.out.println("Monthly Payment: " + (int)(monthlyPayment * 100) / 100.0 );
    System.out.println("Total Payment: " + (int)(monthlyPayment * 12 * numOfYears * 100) / 100.0 + "\n" );
    // Display the header
    System.out.println("Payment#\tInterest\tPrincipal\tBalance");
    int i;
    for (i = 1; i <= numOfYears * 12; i++) {
      interest = (int)(monthlyInterestRate * balance * 100) / 100.0;
      principal = (int)((monthlyPayment - interest) * 100) / 100.0;
      balance = (int)((balance - principal) * 100) / 100.0;
      System.out.println(i + "\t\t" + interest
        + "\t\t" + principal + "\t\t" + balance);
    }
  }
}

近似计算π

π = 4 * （1 - 1/3 + 1/5 - 1/7 + 1/9 -...- 1/(2i - 1) + 1/(2i + 1)

public class Exercise3_30 {
  public static void main(String[] args) {
    double pi = 0;
    double term;
    int sign = 1;
    for (int i = 1; i <= 100000; i++) {
      term = sign * 4.0 / (2 * i - 1);
      pi += term;
      sign = -1 * sign;
      if (i == 10000 || i == 20000 || i == 30000 || i == 40000 ||
          i == 50000 || i == 60000 || i == 70000 || i == 80000 ||
          i == 90000 || i == 100000)
      System.out.println("The PI is " + pi + " for i = " + i);
    }
  }
}

近似计算e

e = 1 + 1/1! + 1/2! + 1/3!+ ...+ 1/i!

新的一项item由前面一个item除以i得到

public class Exercise3_31 {
  public static void main(String[] args) {
    double e = 1;
    double item = 1;
    for (int i = 1; i <= 100000; i++) {
      item = item / i;
      e += item;
      if (i == 10000 || i == 20000 || i == 30000 || i == 40000 ||
          i == 50000 || i == 60000 || i == 70000 || i == 80000 ||
          i == 90000 || i == 100000)
      System.out.println("The e is " + e + " for i = " + i);
    }
  }
}