CS 205 - Programming for the Sciences
Spring 2008 - Practice Exam 1 Answers

Problem 1

Loan calculator

   private void loanPayment_Click(object sender, EventArgs e)
   {
       double amount, annualRate, monthlyRate, payment;
       int years, months;

       // Get user input
       amount = Convert.ToDouble(loanPrincipal.Text);
       annualRate = Convert.ToDouble(loanRate.Text);
       years = Convert.ToInt32(loanTerm.Text);

       // Compute payment
       months = years * 12;
       monthlyRate = annualRate / 12;
       payment = monthlyRate * amount / 
                           (1 - (1 / Math.Pow(1 + monthlyRate, months)));

       // Display results
       results.Items.Add("The monthly payment is " + payment.ToString());
   }

Problem 2

Credit card calculator

   private void minimumPayment_Click(object sender, EventArgs e)
   {
       double currentBalance, monthlyRate, newBalance, minPayment;

       // Get user input
       currentBalance = Convert.ToDouble(cardBalance.Text);
       monthlyRate = Convert.ToDouble(cardRate.Text);

       // Compute this month's balance
       newBalance = currentBalance + currentBalance * monthlyRate;

       // Determine minimum payment
       if (newBalance < 10)
           minPayment = newBalance;
       else
       {
           minPayment = newBalance * .10;
           if (minPayment < 10)
               minPayment = 10;
       }

       // Display results
       results.Items.Add("The mininum payment is " + minPayment.ToString());
   }

Problem 3

Approximation of e. This solution matches the example given with the last term added being the first one below the threshold.

   private void eCalculate_Click(object sender, EventArgs e)
   {
       double sum, term, n, threshold;

       // Get user input
       threshold = Convert.ToDouble(eThreshold.Text);

       // Initialize everything for n = 1, so the sum starts out at 1
       sum = 1;    // Includes 0th term
       n = 1;
       term = 1;   // 0th term

       // Loop until term is under threshold
       while (term >= threshold)
       {
           // Compute next term
           term = term * 1 / n;

           // Add term to sum
           sum = sum + term;

           // Increment n
           n++;
       }

       // Display result
       results.Items.Add("Approximation of e: " + sum.ToString());
   }

This solution is perhaps "better" in the sense that only terms above the threshold are added to the sum.

   private void eCalculate_Click(object sender, EventArgs e)
   {
       double sum, term, n, threshold;

       // Get user input
       threshold = Convert.ToDouble(eThreshold.Text);

       // Initialize everything for n = 0, so the sum starts out at 0
       sum = 0;
       n = 0;
       term = 1;   // 0th term

       // Loop until term is under threshold
       while (term >= threshold)
       {
           // Add term to sum
           sum = sum + term;

           // Increment n
           n++;

           // Compute next term
           term = term * 1 / n;
       }

       // Display result
       results.Items.Add("Approximation of e: " + sum.ToString());
   }