{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Assignment 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this assignment, you will need the information in:\n",
    "\n",
    "* [Expressions](https://matthew-brett.github.io/dsfe/chapters/02/Expressions)\n",
    "* [Names](https://matthew-brett.github.io/dsfe/chapters/02/Names)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Don't forget to execute the cells in the notebook, that I've written for you."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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."
   ]
  },
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "For example, try executing the following cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This is just a comment.  Python ignores it.  It's just for show."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nothing happens - Python ignored everything after the hash character."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The problem is my bank.\n",
    "\n",
    "I have a credit card debt of £500.\n",
    "\n",
    "Let's give that debt amount, a *name*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This is the amount I owe at the moment\n",
    "my_debt = 500"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At the moment, the bank is nice enough to charge me 10% interest per year.   Let's give that a name too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "interest_rate = 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The amount of interest, after one year, is therefore:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "50.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "interest = my_debt * interest_rate\n",
    "interest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then my total new debt will be:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "550.0"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_debt + interest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I can also calculate my total new debt all in one go by multiplying by `1 + interest_rate` - in my case - `1.1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "debt_increaser = 1 + interest_rate\n",
    "debt_increaser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "550.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "my_debt * debt_increaser"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Now your turn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Add your code to the cell below, and execute it, to show my total debt after two years.  Your code will probably start with:\n",
    "\n",
    "```\n",
    "my_debt * debt_increaser\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Show my debt after two years.\n",
    "# Your code below this comment"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fill in the next cell, in the same way, to show my debt after three years."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Show my debt after three years."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now show my debt after 10 years.   You might want to use the *power* operator `**` to do this."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Show my debt after ten years."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An offer from the bank"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The bank has just sent me a nice 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?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is their proposed weekly interest rate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0018867924528301887"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weekly_interest_rate = interest_rate / 53\n",
    "weekly_interest_rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That corresponds to:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0018867924528303"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weekly_debt_increaser = 1 + weekly_interest_rate\n",
    "weekly_debt_increaser"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, starting from my original debt, I will owe this much after one week:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "500.94339622641513"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# What I owe, after one week, on the new deal\n",
    "my_debt * weekly_debt_increaser"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fill in the cell below, to show how much I will owe after 52 weeks.  You will probably want `**` here again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Show my debt after 52 weeks, on the new deal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For extra cool points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code to estimate the right weekly interest rate."
   ]
  }
 ],
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