Group Problem (20 minutes)

With a partner, write a Python program that uses the compound interest formula (see below) to tell the user how much money will be in a bank account after 10 years when the initial balance is $1000, the interest rate is 5% and the interest is compounded quarterly.

Compound Interest

  • A = amount of money accumulated after n years, including interest
  • P = principal amount (the initial amount you borrow or deposit)
  • r = annual rate of interest (as a decimal)
  • n = number of times the interest is compunded per year
  • t = number of years the money is deposited or borrowed

Example:

  • P = $1500
  • r = 0.043
  • n = 4 (i.e., compounded quarterly)
  • t = 6 years
  • A = approx. $1938.84

Let’s begin by setting up a new Python file and calling it “compound.py” (see Lesson 2 if you can’t remember how to do this).

A good place to start with any program is by using comments to map out a possible plan. Our program for this problem will be fairly similar to the quadratic formula problem we solved yesterday. This means that with will have three sections to our program: 1) defining variables, 2) calculating the compound interest, and 3) printing the result to the screen.

Let’s start our program by adding these comments to our program:

# compound.py

# Define variables


# compound interest calculation


# print result to screen

We can now use these comments as our work plan. The first section to work on is the compound interest calculation. So let’s turn the compound interest formula into Python.

# compound.py

# Define variables


# compound interest calculation
A = P * (1 + (r / n)) ** (n * t)

# print result to screen

Then, we can define our variables. Since we have an example above, we can use these sample values to test whether our formula is correct.

# compound.py

# Define variables
P = 1500    # initial amount
r = .043    # annual rate of interest
n = 4       # number of times interest is compounded per year
t = 6       # number of years

# compound interest calculation
A = P * (1 + (r / n)) ** (n * t)

# print result to screen

Next, we need to add a print statement to output our result. For now, we’ll add the simple print statement, print(A), and run our program to test it.

Since we didn’t get any bugs and did get the right result (though our answer is a much longer float), we can now enter the new values for the specific problem we are trying to solve. We can also make our print() statement more user-friendly.

# compound.py

# Define variables
P = 1000    # initial amount
r = .05     # annual rate of interest
n = 4       # number of times interest is compounded per year
t = 10      # number of years

# compound interest calculation
A = P * (1 + (r / n)) ** (n * t)

# print result to screen
print("The amount accumulated:", A, "dollars.")

Types of Errors

The three most commonly occuring types of errors in Python are these:

  • syntax errors - occur when something is wrong with the structure of the program; this is usually the result of a typo, a missing parenthesis, etc.
  • runtime errors - occur when the program begins running without syntax errors but does not finish; the most common cause is an undefined variable or a misspelled variable name
  • semantic errors - occurs when the program runs and ends, but the result is incorrect; these are the hardest to debug because there are no error messages to help us

So, using our compound.py program, introduce a syntax error, a runtime error, and a semantic error.

More Calculation Problems

Write a Python program to solve the following problems.

Volume of a Sphere Problem

The volume of a sphere with radius r is (4/3)πr^3. What is the volume of a sphere with radius of 5?

# volume.py
# define variables
radius = 5

# calculate volume
volume = (4 / 3) * 3.1415 * radius ** 3

# print result to screen
print("The volume of a sphere with radius of " + str(radius) + " is " + str(volume) + ".")

Book Price Problem

Suppose the cover price of a book is $24.95, but bookstores get a 40% discount. Shipping costs $3 for the first copy and 75 cents for each additional copy. What is the total wholesale cost for 60 copies?

# books.py

# assign variables
price = 24.95
discount = .4
copies = 60

# run calculations
book_price = price * (1 - discount) * copies 
shipping = 3 + (copies - 1) * .75
total = book_price + shipping

# print results
print("The total cost for " + str(copies) + " copies is $" + str(round(total,2)) + ".")

Homework:

Begin working on Project 1