bicubic/Interest Free Loans

## Interest Free Loans
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Australia, we have interest-free loans for higher education. These are indexed against CPI to match inflation and have a mandatory repayment which is a bracketed percentage of your income. They also come with the option to make a voluntary contribution which enjoys a 10% discount. \n",
    "\n",
    "The following is my attempt to work out whether its better to make a full voluntary repayment or to keep the cash in a savings account. \n",
    "\n",
    "Some assumptions:\n",
    "* Debt is at 50k\n",
    "* The person in this scenario already has enough cash in a savings account to repay the loan in full\n",
    "* The mandatory repayment is 1k/month\n",
    "* The income of the person is facored out, so we'll assume its exactly equal to the mandatory repayment for this\n",
    "* CPI growth and inflation are both IGNORED. I am not sure this is a valid assumption\n",
    "* Interest on savings accounts is 2% annual, compounding monthly\n",
    "* A 10% discount is offered on a voluntary repayment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "plt.style.use('ggplot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "monthly_repayment = 1000.0 #mandatory monthly repayment, and amount of funds available to invest\n",
    "debt = 50000 #debt outstanding\n",
    "mean_cpi_growth = 0.22 #mean CPI growth for indexing. This is presently IGNORED\n",
    "voluntary_discount = 0.1 #10% discount on voluntary repayments\n",
    "\n",
    "cash_on_hand = debt #The savings acount has exactly enough cash to repay the loan in full \n",
    "savings_interest = 0.02 #Assume a 2% interest on the savings account where the cash is parked\n",
    "monthly_income = monthly_repayment #We make exactly enough money to do the monthly repayment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x140fd080>"
      ]
     },
     "execution_count": 161,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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j4j2cvvEmTq5cyomf/T/CH/gxoVf283dVASMsLCy43g/NpHFpWLCPy+rVq31fJyQkkJCQ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\ngYiIAP8fLe4TzmB47sUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13e77208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#first of all, lets figure out how long it'll take to pay down the debt\n",
    "outstanding = debt\n",
    "points = []\n",
    "i=0\n",
    "while(outstanding>0):\n",
    "    repayment = monthly_repayment #assume no inflation - (monthly_repayment*mean_cpi_growth)\n",
    "    outstanding-=repayment\n",
    "    i+=1\n",
    "    points.append({'month': i, 'outstanding': outstanding})\n",
    "    \n",
    "df_base = pd.DataFrame(points[:-1]).set_index('month')\n",
    "df_base.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49"
      ]
     },
     "execution_count": 162,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "months_to_pay = max(df_base.index)\n",
    "months_to_pay"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulate the 'minimum repayment' scenario:\n",
    "* Start at <b>cash</b>=<b>debt</b>\n",
    "* Calculate monthly compouinding interest on <b>cash</b>\n",
    "* After month <b>months_to_pay</b>, start adding <b>monthly_income</b> to <b>cash</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x14634208>"
      ]
     },
     "execution_count": 163,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JCSFEl1D/2II68h1a0lIZyeRFJCSEEJ2m/rUL9fG77hPV/fsbXY7oQhISQohO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\n2XXs5ZAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x143ec3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = []\n",
    "v = cash_on_hand\n",
    "for month in range(0, months_to_pay*2):\n",
    "    if (month > months_to_pay):\n",
    "        v = v + monthly_income\n",
    "    v = v + savings_interest * v / 12.0 #this is a NAIIVE interest compounding. Not strictly correct!\n",
    "    points.append({'month': month, 'value_minimum': v})\n",
    "df_slow = pd.DataFrame(points)\n",
    "df_slow.set_index('month').plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulate the 'early voluntary repayment' scenario:\n",
    "<br/>\n",
    "To sanity-check, we will assume a <b>voluntary_discount</b> of 0, in which case both scenarios should be roughly equal\n",
    "* Start at <b>cash</b>=<b>debt</b> * <b>voluntary_discount</b>\n",
    "* Calculate monthly compouinding interest on <b>cash</b>\n",
    "* After month <b>0</b>, start adding <b>monthly_income</b> to <b>cash</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x14816a20>"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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gnjSmnjQWLD0xnlrMK8sx77zhn2+pyg6DVqrN4XCQnp5+2NeOOFX4ww8/zMcff8w333yD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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x145303c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = []\n",
    "v = cash_on_hand * voluntary_discount * 0 #we just lost eaxctly 90% of our cash on hand\n",
    "for month in range(0, months_to_pay*2):\n",
    "    v = v + monthly_income \n",
    "    v = v + savings_interest * v / 12.0 #this is a NAIIVE interest compounding. Not correct!\n",
    "    points.append({'month': month, 'value_voluntary': v})\n",
    "df_fast = pd.DataFrame(points)\n",
    "df_fast.set_index('month').plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets check how the two scenarios compare "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_voluntary</th>\n",
       "      <th>value_minimum</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1001.666667</td>\n",
       "      <td>50083.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2005.002778</td>\n",
       "      <td>50166.805556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3010.011116</td>\n",
       "      <td>50250.416898</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4016.694468</td>\n",
       "      <td>50334.167593</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5025.055625</td>\n",
       "      <td>50418.057872</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       value_voluntary  value_minimum\n",
       "month                                \n",
       "0          1001.666667   50083.333333\n",
       "1          2005.002778   50166.805556\n",
       "2          3010.011116   50250.416898\n",
       "3          4016.694468   50334.167593\n",
       "4          5025.055625   50418.057872"
      ]
     },
     "execution_count": 165,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_combined = df_fast.set_index('month').join(df_slow.set_index('month'))\n",
    "df_combined.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x14b9ac18>"
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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JE9jmP43auhn9kX+iT3kYzVeaoa8UTZV0M6qhDRs28MMPP6DrOkFBQTz88MMU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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x140ee240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the two scenarios on the same axis\n",
    "df_combined.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The two scenarios should have become identical at month=<b>months_to_pay</b>, however there's some minor difference here. I'm assuming due to the fact that I'm working with integer months. The fact that the scenarios become parallel is good enough.\n",
    "\n",
    "---\n",
    "\n",
    "Now lets factor in a 10% voluntary payment discount rate, meaning we start at cash=<b>deb</b>*0.1 and immediately begin compounding interest with monthly deposits of <b>monthly_income</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x154cc048>"
      ]
     },
     "execution_count": 173,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Zjv2zsrIICgqqcOdQfnvZPpmZmZhMJqxWKwUFBU7vIsqfTBl3XyTk9wwGWTjl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\nCCGq9P/mgxlfywazVQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14e8b9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = []\n",
    "v = cash_on_hand * voluntary_discount * 1.0\n",
    "for month in range(0, months_to_pay*2):\n",
    "    v = v + monthly_income \n",
    "    v = v + savings_interest * v / 12.0 #this is a NAIIVE interest compounding. Not correct!\n",
    "    points.append({'month': month, 'value_voluntary': v})\n",
    "df_fast = pd.DataFrame(points)\n",
    "df_combined = df_fast.set_index('month').join(df_slow.set_index('month'))\n",
    "df_combined.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x159036a0>"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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0aRODBw8GIC8vj/z8fGzbJjMzk5SU5ov+HDhwgJycHBoaGkhNTSUzMxOAhoYG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\nFiIiEpLCQkREQlJYiIhISAoLEREJ6f8HGYAIjGP8bVgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x14e8b748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the value difference of the two scenarios\n",
    "df_combined['voluntary_difference'] = df_combined.value_voluntary - df_combined.value_minimum\n",
    "df_combined.voluntary_difference.plot()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value_voluntary</th>\n",
       "      <th>value_minimum</th>\n",
       "      <th>voluntary_difference</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>107688.615708</td>\n",
       "      <td>104162.774053</td>\n",
       "      <td>3525.841655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>108869.763401</td>\n",
       "      <td>105338.045343</td>\n",
       "      <td>3531.718058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>110052.879673</td>\n",
       "      <td>106515.275419</td>\n",
       "      <td>3537.604255</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>111237.967806</td>\n",
       "      <td>107694.467544</td>\n",
       "      <td>3543.500262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>112425.031086</td>\n",
       "      <td>108875.624990</td>\n",
       "      <td>3549.406096</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       value_voluntary  value_minimum  voluntary_difference\n",
       "month                                                      \n",
       "93       107688.615708  104162.774053           3525.841655\n",
       "94       108869.763401  105338.045343           3531.718058\n",
       "95       110052.879673  106515.275419           3537.604255\n",
       "96       111237.967806  107694.467544           3543.500262\n",
       "97       112425.031086  108875.624990           3549.406096"
      ]
     },
     "execution_count": 175,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_combined.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the difference between the two scenarios seems to be a more or less flat 3.5k in favour of the voluntary repayment scenario. Now how to derrive this number?!"
   ]
  }
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