Interesting, no?

For this assignment, you will probably eventually need the power operator.

As in introduction, the multiplication operator is the * sign, as in:

10.50 * 3

31.5

It tells Python to multiply the values on the left by the value on the right.

The power operator is **. It works like this:

2 ** 4

16

The line above tells Python to calculate the number to the left (here 2) to the power of the number to the right, here 4. In other words, the calculation 2 ** 4 in Python is the same as:

2 * 2 * 2 * 2

16

Likewise:

3.5 ** 5

525.21875

results in the same calculation as:

3.5 * 3.5 * 3.5 * 3.5 * 3.5

525.21875

Don’t forget to execute the cells in the notebook, that we have written for you.

Comments

In what follows, you will see me using comments. Comments start with a hash character - #. Python ignores everything after the hash character. This is useful to write text for you or others to read, inside your code.

For example, try executing the following cell.

# This is just a comment.  Python ignores it.  It's just for show.

Nothing happens - Python ignored everything after the hash character.

The problem

The problem is my bank.

At the beginning of this year, I have a credit card debt of £500. Call this year the first year, or year 1.

At the moment, the bank will charge me 10% interest per year.

At the end of the first year, the bank will add 10% to my current debt of £500, so my new debt, at the start of the second year, will be £550.

At the end of the second year, the bank will add 10% of my debt of £550. 10% of £550 is £55, so my debt at the start of the third year is £605.

Let’s give my original debt amount, a name:

# This is the amount I owe at the beginning of the first year.
my_debt = 500

The bank charges 10% interest per year. Put another way, they calculate the interest by multiplying my current debt by 0.1. Let’s give that a name too.

interest_rate = 0.1

The amount of interest at the end of the first year is therefore:

interest = my_debt * interest_rate
interest

50.0

Then my total new debt at the start of the second year will be:

my_debt + interest

550.0

There is a short cut to calculate my total debt at the start of the second year.

Remember the total debt is the original debt plus interest, which is my_debt + my_debt * interest_rate. I could also write this as my_debt * 1 + my_debt * interest_rate, and this is also equal to my_debt * (1 + interest_rate).

Now make a new variable debt_increaser that is equal to 1 + interest_rate.

debt_increaser = 1 + interest_rate
debt_increaser

1.1

This variable allows me to calculate my_debt + my_debt * interest_rate in a more compact way, like this:

my_debt * debt_increaser

550.0

Because of the definition of debt_increaser above, this is mathematically equal to my_debt * (1 + interest_rate), which in turn is mathematically equal to my_debt * 1 + my_debt * interest_rate which is my_debt + my_debt * interest_rate - the calculation we want.

Now your turn

Add your code to the cell below, and execute it, to show my total debt at the beginning of the third year. Your code will probably start with:

my_debt * debt_increaser

You should get the same answer as the table above.

# Show my debt after two years.
# Your code below this comment

Fill in the next cell, in the same way, to show my debt at the beginning of the fourth year.

# Show my debt at the beginning of the fourth year.

You might want to use a pencil and paper to do the calculation that continues from the table above, to check your answer is correct.

Now show my debt after 10 years - at the beginning of the eleventh year. You might want to use the power operator ** to do this. If you need a refresher on powers, you may remember that, if I have some number x then x ** 4 (read as “x to the power of four”) is another way of writing `x * x * x

• x`.

# Show my debt at the beginning of the eleventh year.

An offer from the bank

The bank has just sent me a friendly letter explaining that they are going to start charging me interest every week instead of every year. They value me as a customer, so, instead of dividing the annual interest rate by 52, they are going to divide it by 53 instead. But - is that a good offer?

Here is their proposed weekly interest rate:

weekly_interest_rate = interest_rate / 53
weekly_interest_rate

0.0018867924528301887

That corresponds to:

weekly_debt_increaser = 1 + weekly_interest_rate
weekly_debt_increaser

1.0018867924528303

So, starting from my original debt, I will owe this much after one week:

# What I owe, after one week, on the new deal
my_debt * weekly_debt_increaser

500.94339622641513

Fill in the cell below, to show how much I will owe after 52 weeks. You will probably want ** here again.

# Show my debt after 52 weeks, on the new deal

For extra cool points

Can you calculate roughly what the weekly interest rate has to be, in order to correspond to the 10% annual interest that I started with? There are several ways to do this, but you can try trial and error, if you like.

Note - this is relatively hard, so don’t worry if it is not obvious how to do this.

# Your code to estimate the right weekly interest rate.