Generating compound interest with integers

[David Herron]

I am trying to change this code to use only integers to calculate the compound interest.

// Compound-interest calculations with for.



public class Interest 

{

   public static void main( String args[] )

   {

      double amount; // amount on deposit at end of each year

      double principal = 1000.0; // initial amount before interest

      double rate = 0.05; // interest rate



      // display headers

      System.out.printf( "%s%20s\n", "Year", "Amount on deposit" );



      // calculate amount on deposit for each of ten years

      for ( int year = 1; year <= 10; year++ ) 

      {

         // calculate new amount for specified year

         amount = principal * Math.pow( 1.0 + rate, year );



         // display the year and the amount

         System.out.printf( "%4d%,20.2f\n", year, amount );

      } // end for

   } // end main

} // end class Interest

This is what I have so far,

public class Interest 
{
    public static void main(String[] args) {
        int amount;
        int principal = 100000;
        int rate = 5;
        
        System.out.printf("%s%20s\n", "Year", "Amount on deposit");
        
        for (int year = 1; year <= 10; year++)
        {
            amount = (principal * (int)Math.pow(100 + rate, year)) / (int)Math.pow(100, year);
            
            System.out.printf("%4d%20s\n", year, amount);
        }
  

And here is the output I get,



Why do I get the output after year 2? I assume it has something to do with the remainder.

I also have to format this output with the decimal point, etc.. which I think I will be ok with after I get through this part.
Thanks!

[Campbell Ritchie]

Are you really taking powers of 105 or similar? Then you get 100000 × 105 × 105 which is 1102500000. Now next time you multiply by 105, you get an overflow error. Meanwhile the divisor is continuing to increase, and when the divisor is larger than the dividend, your integer division gives 0.

I am not sure what to recommend. You could try using long arithmetic, but that will eventually run out of space. The best way to calculate money is with the BigDecimal class.

[David Herron]

I realize these numbers are huge and I figured that was possibly the issue. I guess I am taking the problem too literally.

After the book shows this program as an example, it goes on to say that this (using double) is not the best method for achieving accurate results, then it states "you've been warned!". It never gives a solution apart from a quick reference to the existence of BigDecimal but not how to use it.

Then I am given this problem, so that how I got here!

Thanks! I will go the BigDecimal route!

[Campbell Ritchie]

import java.math.BigDecimal;
import java.util.Scanner;

public class BigDecimalDemo
{
    private final BigDecimal number1;
    private final BigDecimal number2;

    public BigDecimalDemo(BigDecimal number1, BigDecimal number2)
    {
        this.number1 = number1;
        this.number2 = number2;
    }

    public BigDecimalDemo(String entry1, String entry2)
    {
        this(new BigDecimal(entry1), new BigDecimal(entry2));
    }

    private void ShowOperations()
    {
        BigDecimal sum = number1.add(number2);
        BigDecimal difference = number1.subtract(number2);
        BigDecimal product = number1.multiply(number2);
        BigDecimal quotient = number1.divide(number2);
        BigDecimal remainder = number1.remainder(number2);
        System.out.printf(
                "%f + %f = %f%n%1$f - %2$f = %f%n%1$f \u00d7 %2$f = %f%n" +
                "%1$f \u00f7 %2$f = %f%n%1$f %% %2$f = %f%n",
                number1, number2, sum, difference, product, quotient, remainder);
    }

    public static void main(String[] args)
    {
        if (args.length < 2)
        {
            System.out.println(
               "No command-line arguments: enter two numbers eg 1.23 45.678: ");
            args = new Scanner(System.in).nextLine().split("\\s");
        }
        new BigDecimalDemo(args[0], args[1]).ShowOperations();
    }
}

java BigDecimalDemo
No command-line arguments: enter two numbers eg 1.23 45.678:
39856398.767624534 0.00625
39856398.767625 + 0.006250 = 39856398.773875
39856398.767625 - 0.006250 = 39856398.761375
39856398.767625 × 0.006250 = 249102.492298
39856398.767625 ÷ 0.006250 = 6377023802.819925
39856398.767625 % 0.006250 = 0.005125

Note the %f tag defaults to 6 decimal places.
So far, so good. You can get 1 from 0.00625 if you repeatedly multiply by 2 or 5, so the division will eventually come out exactly. But what if the division isn't exact?

java BigDecimalDemo 9.0 0.7
Exception in thread "main" java.lang.ArithmeticException: Non-terminating decimal expansion; no exact representable decimal result.
at java.math.BigDecimal.divide(BigDecimal.java:1616)
at BigDecimalDemo.ShowOperations(BigDecimalDemo.java:25)
at BigDecimalDemo.main(BigDecimalDemo.java:41)

We now need a version 2.

import java.math.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;
import java.util.Scanner;

public class BigDecimalDemo
{
    private final BigDecimal number1;
    private final BigDecimal number2;

    public BigDecimalDemo(BigDecimal number1, BigDecimal number2)
    {
        this.number1 = number1;
        this.number2 = number2;
    }

    public BigDecimalDemo(String entry1, String entry2)
    {
        this(new BigDecimal(entry1), new BigDecimal(entry2));
    }

    private void ShowOperations()
    {
        BigDecimal sum = number1.add(number2);
        BigDecimal difference = number1.subtract(number2);
        BigDecimal product = number1.multiply(number2);
        MathContext rndUpDp4 = new MathContext(4, RoundingMode.HALF_UP);
        BigDecimal quotient = number1.divide(number2, rndUpDp4);
        BigDecimal remainder = number1.remainder(number2);
        System.out.printf(
                "%f + %f = %f%n%1$f - %2$f = %f%n%1$f \u00d7 %2$f = %f%n" +
                "%1$f \u00f7 %2$f = %f%n%1$f %% %2$f = %f%n",
                number1, number2, sum, difference, product, quotient, remainder);
    }

    public static void main(String[] args)
    {
        if (args.length < 2)
        {
            System.out.println(
               "No command-line arguments: enter two numbers eg 1.23 45.678: ");
            args = new Scanner(System.in).nextLine().split("\\s");
        }
        new BigDecimalDemo(args[0], args[1]).ShowOperations();
    }
}

Apart from the imports, the change is on lines 27-28. You supply a rounding mode and a precision. In this case 4 appears to mean 4 significant figures, not four places after the decimal point. If you try to find the divide() method, you find it is overloaded about 6 times to allow for that problem. Any overloading can be used, but they may give slightly different results.
Another thing is, BigDecimal is an immutable class. You will see the values of number1 and number2 do not change in the arithmetic.
Its equals() method includes the scale as well as the value, so 1.0 and 1.00 are not the same, but new BigDecimal("1.0").compareTo(new BigDecimal("1.000") will return 0, so you can use the compareTo method.
Don't use the constructor which takes a double, but use one of the other constructors. You can see if you try System.out.println(new BigDecimal(1.23)); and with "1.23", and see the differences.
Read the BigDecimal and RoundingMode and MathContext documentation.

[Campbell Ritchie]

There is a recent discussion about problems with double and BigDecimal here.

[David Herron]

Thank you for this. More than thorough. I now have this code to reference. Upon further reading, I realized the assignment is not asking us to implement BigDecimal. But since this is the proper way to do things i will be going over it as well as the RoundingMode and MathContext documentation.

Thank you again!

[Campbell Ritchie]

You're welcome

[Campbell Ritchie]

Last year, I wrote: . . . the divide() method . . . is overloaded about 6 times to allow for that problem. Any overloading can be used, but they may give slightly different results. . . .

So, try this:

        BigDecimal quotient = number1.divide(number2, 4, RoundingMode.HALF_UP);

. . . as an alternative to line 27 above. That seems to give 4 places after the decimal point.

[Campbell Ritchie]

In the first post in this thread, the image has vanished. I think it shou‍ld be a printout like this

java Interest
Year   Amount on deposit
   1              105000
   2              110250
   3                -201
   4                   3
   5                   0
   6                   0
   7                   0
   8                   0
   9                   0
  10                   0

That is another reason for not using screenshots: text posted doesn't mysteriously vanish.