4003-231: CS1		Homework Programs #1		Due: Thur. week 4

		      ASSIGNMENT & EXPRESSIONS

======================== Grading Policy ================================

Each question below has a number of points associated with it, you are
required to turn in 3 points worth of problems.

===================== Things to Turn in ================================

You should turn in a printout of your program (make sure you name and
the homework number is at the top.  In addition, you should turn in a
printout of the running of your program.

To get a file that contains the output of everything that is printed on
the screen (in Unix) you can use the "script" command.  For information
on how to use the command type
	man script
on the Unix command line.

When providing output from your program you should run your program
multiple times, with a couple of the runs using data not provided in
the examples.

===================== Homework Programs #1 =============================

1. (1 pt) Write a program which asks the user to enter a double and then 
   prints out the number truncated to two decimal places.

        For example: 
        32.4851 would truncated to 32.48
        72.9431 would truncated to 72.94
        54.0000 would truncated to 54.00
         4.9999 would truncated to  4.99

   Your program should just use type conversions and arithmetic to
   round the number.  For example:

	32.4851 is the number I want to truncate.
	32.4851 * 100 gives 3248.51
	with 3248.51 if I drop the fractional part I get 3248
	3248 / 100 gives 32.48, which is the result.


2. (1 pt) Modify the program you wrote in problem 1 above to round the 
   number instead of truncating it.

        For example: 
        32.4851 would rounded to 32.49
        72.9431 would rounded to 72.94
        54.0000 would rounded to 54.00
         4.9999 would rounded to  5.00


3. (2 pts) Write a program that computes the monthly payment of an 
   amortized loan (such as a mortgage or student loan) and the total 
   interest paid during the life of the loan.

   The program should ask for the following information from the user:
	1. The amount of the loan
	2. The yearly interest rate, such as 7.75%
	3. The term of the loan in years

   The program should then calculate the payment of the loan and the total 
   interest for the full term and print out these values.  The formula for
   the monthly payment of an amortized loan is the following:

                           int
        Pmt = Amt * -------------------
                                    -n
                     1 - ( 1 + int )
   where:
        Pmt             The monthly payment
        Amt             Amount of the loan
        int             Interest for one month
        n               Term of the loan in months

   Note: the bottom of the equation is 1 minus the quantity (1 + int) 
   raised to the negative n'th power.

   To calculate the total interest paid for a full term loan, use the 
   formula:

        Pmt * n - Amt

   Input
   -----
   The program must ask for the amount of the loan, the interest rate as a
   percentage and the term in years.  Note the differences between the 
   units of the input items and those used in the formula.

   Output
   ------
   The program should print out a sign-on message stating what it does, 
   prompt the user for the required values and print the monthly payment 
   and total interest.  When you run the program, the output should look 
   like:

        Loan amortization program

        Enter the loan amount: 25000
        Enter the interest rate (like 7.25): 8.25
        Enter loan term in years: 5

        Loan amount = $25000.00, at 8.25% for 5 years

        Monthly payment = $509.9062916328536
        Total interest  = $5594.377497971214

   Another example run looks like this:

        Loan amortization program

        Enter the loan amount: 100001
        Enter the interest rate (like 7.25): 4.975
        Enter loan term in years: 30

        Loan amount = $100001.0, at 4.975% for 30 years

        Monthly payment = $535.3001220611827
        Total interest  = $92707.04394202578

   Notes
   -----
   To raise x to the power of y, you can use the "pow" method in the
   standard Math class.  Calling 
	z = Math.pow( x, y ) 
   raises x to the y power and saves the result in the variable z. 


4. (3 pts) Modify the loan program in problem 3 above to round the 
   numbers to two decimal places prior to printing them out.  Note you 
   want to round the numbers only at the last possible moment to 
   minimize rounding error.