02_saving.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Saving for Retirement\n",
    "- Let's assume we want to save $10,000 every year\n",
    "- Our initial balance is zero\n",
    "- How much would our account grow over 30 years if we earn a rate of 5%?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: numpy_financial in d:\\bbcx-investments-quarto\\quarto\\venv\\lib\\site-packages (1.0.0)\n",
      "Requirement already satisfied: numpy>=1.15 in d:\\bbcx-investments-quarto\\quarto\\venv\\lib\\site-packages (from numpy_financial) (1.23.2)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\n",
      "[notice] A new release of pip available: 22.2.1 -> 23.3.2\n",
      "[notice] To update, run: python.exe -m pip install --upgrade pip\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "!pip install numpy_financial\n",
    "import numpy_financial as npf\n",
    "import plotly.graph_objects as go"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>begbal</th>\n",
       "      <th>capgain</th>\n",
       "      <th>deposit</th>\n",
       "      <th>endbal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>$0.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$10,000.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$500.00</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$20,500.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>$20,500.00</td>\n",
       "      <td>$1,025.00</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$31,525.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>$31,525.00</td>\n",
       "      <td>$1,576.25</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$43,101.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>$43,101.25</td>\n",
       "      <td>$2,155.06</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$55,256.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>$55,256.31</td>\n",
       "      <td>$2,762.82</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$68,019.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>$68,019.13</td>\n",
       "      <td>$3,400.96</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$81,420.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>$81,420.08</td>\n",
       "      <td>$4,071.00</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$95,491.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>$95,491.09</td>\n",
       "      <td>$4,774.55</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$110,265.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>$110,265.64</td>\n",
       "      <td>$5,513.28</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$125,778.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>$125,778.93</td>\n",
       "      <td>$6,288.95</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$142,067.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>$142,067.87</td>\n",
       "      <td>$7,103.39</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$159,171.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>$159,171.27</td>\n",
       "      <td>$7,958.56</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$177,129.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>$177,129.83</td>\n",
       "      <td>$8,856.49</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$195,986.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>$195,986.32</td>\n",
       "      <td>$9,799.32</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$215,785.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>$215,785.64</td>\n",
       "      <td>$10,789.28</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$236,574.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>$236,574.92</td>\n",
       "      <td>$11,828.75</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$258,403.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>$258,403.66</td>\n",
       "      <td>$12,920.18</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$281,323.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>$281,323.85</td>\n",
       "      <td>$14,066.19</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$305,390.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>$305,390.04</td>\n",
       "      <td>$15,269.50</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$330,659.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>$330,659.54</td>\n",
       "      <td>$16,532.98</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$357,192.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>$357,192.52</td>\n",
       "      <td>$17,859.63</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$385,052.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>$385,052.14</td>\n",
       "      <td>$19,252.61</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$414,304.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>$414,304.75</td>\n",
       "      <td>$20,715.24</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$445,019.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>$445,019.99</td>\n",
       "      <td>$22,251.00</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$477,270.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>$477,270.99</td>\n",
       "      <td>$23,863.55</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$511,134.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>$511,134.54</td>\n",
       "      <td>$25,556.73</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$546,691.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>$546,691.26</td>\n",
       "      <td>$27,334.56</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$584,025.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>$584,025.83</td>\n",
       "      <td>$29,201.29</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$623,227.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>$623,227.12</td>\n",
       "      <td>$31,161.36</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$664,388.48</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        begbal    capgain    deposit      endbal\n",
       "1        $0.00      $0.00 $10,000.00  $10,000.00\n",
       "2   $10,000.00    $500.00 $10,000.00  $20,500.00\n",
       "3   $20,500.00  $1,025.00 $10,000.00  $31,525.00\n",
       "4   $31,525.00  $1,576.25 $10,000.00  $43,101.25\n",
       "5   $43,101.25  $2,155.06 $10,000.00  $55,256.31\n",
       "6   $55,256.31  $2,762.82 $10,000.00  $68,019.13\n",
       "7   $68,019.13  $3,400.96 $10,000.00  $81,420.08\n",
       "8   $81,420.08  $4,071.00 $10,000.00  $95,491.09\n",
       "9   $95,491.09  $4,774.55 $10,000.00 $110,265.64\n",
       "10 $110,265.64  $5,513.28 $10,000.00 $125,778.93\n",
       "11 $125,778.93  $6,288.95 $10,000.00 $142,067.87\n",
       "12 $142,067.87  $7,103.39 $10,000.00 $159,171.27\n",
       "13 $159,171.27  $7,958.56 $10,000.00 $177,129.83\n",
       "14 $177,129.83  $8,856.49 $10,000.00 $195,986.32\n",
       "15 $195,986.32  $9,799.32 $10,000.00 $215,785.64\n",
       "16 $215,785.64 $10,789.28 $10,000.00 $236,574.92\n",
       "17 $236,574.92 $11,828.75 $10,000.00 $258,403.66\n",
       "18 $258,403.66 $12,920.18 $10,000.00 $281,323.85\n",
       "19 $281,323.85 $14,066.19 $10,000.00 $305,390.04\n",
       "20 $305,390.04 $15,269.50 $10,000.00 $330,659.54\n",
       "21 $330,659.54 $16,532.98 $10,000.00 $357,192.52\n",
       "22 $357,192.52 $17,859.63 $10,000.00 $385,052.14\n",
       "23 $385,052.14 $19,252.61 $10,000.00 $414,304.75\n",
       "24 $414,304.75 $20,715.24 $10,000.00 $445,019.99\n",
       "25 $445,019.99 $22,251.00 $10,000.00 $477,270.99\n",
       "26 $477,270.99 $23,863.55 $10,000.00 $511,134.54\n",
       "27 $511,134.54 $25,556.73 $10,000.00 $546,691.26\n",
       "28 $546,691.26 $27,334.56 $10,000.00 $584,025.83\n",
       "29 $584,025.83 $29,201.29 $10,000.00 $623,227.12\n",
       "30 $623,227.12 $31,161.36 $10,000.00 $664,388.48"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RATE     = 0.05\n",
    "N_SAVING = 30\n",
    "PMT      = 10000.0\n",
    "PV       = 0.0\n",
    "\n",
    "acct = pd.DataFrame(dtype=float,columns=['begbal','capgain','deposit','endbal'],index=np.arange(1,N_SAVING+1))\n",
    "acct.deposit = PMT\n",
    "for t in acct.index:\n",
    "    if t==1:\n",
    "        acct.loc[t,'begbal'] = PV\n",
    "    else:\n",
    "        acct.loc[t,'begbal'] = acct.loc[t-1,'endbal']\n",
    "    acct.loc[t,'capgain'] = acct.loc[t,'begbal']*RATE\n",
    "    acct.loc[t,'endbal'] = acct.loc[t,'begbal'] + acct.loc[t,'capgain'] + acct.loc[t,'deposit']\n",
    "\n",
    "pd.options.display.float_format = '${:,.2f}'.format\n",
    "acct"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "664388.4750301335"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Of course, we could do this in one step using a financial function\n",
    "npf.fv(RATE, N_SAVING, -PMT, -PV)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# If we wanted to be able to withdraw $W=100,000 each year for 20 years, \n",
    "# how much do we need to save for the first 30 years\n",
    "\n",
    "WITHDRAWAL = 100000.0\n",
    "N_WITHDRAW = 20\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1,246,221.03\n"
     ]
    }
   ],
   "source": [
    "# First, we find how much we'd need to have saved as of t=30:\n",
    "\n",
    "end_savings_bal = npf.pv(RATE,N_WITHDRAW,-WITHDRAWAL,0)\n",
    "print(f'{end_savings_bal:,.2f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "18,757.41\n"
     ]
    }
   ],
   "source": [
    "# Second, we solve a PMT problem to determine the amount we need to save:\n",
    "\n",
    "pmt = npf.pmt(RATE,N_SAVING,PV,-end_savings_bal)\n",
    "print(f'{pmt:,.2f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>begbal</th>\n",
       "      <th>capgain</th>\n",
       "      <th>deposit</th>\n",
       "      <th>withdraw</th>\n",
       "      <th>endbal</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>$0.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$10,000.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$500.00</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$20,500.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>$20,500.00</td>\n",
       "      <td>$1,025.00</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$31,525.00</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>$31,525.00</td>\n",
       "      <td>$1,576.25</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$43,101.25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>$43,101.25</td>\n",
       "      <td>$2,155.06</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$55,256.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>$55,256.31</td>\n",
       "      <td>$2,762.82</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$68,019.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>$68,019.13</td>\n",
       "      <td>$3,400.96</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$81,420.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>$81,420.08</td>\n",
       "      <td>$4,071.00</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$95,491.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>$95,491.09</td>\n",
       "      <td>$4,774.55</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$110,265.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>$110,265.64</td>\n",
       "      <td>$5,513.28</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$125,778.93</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>$125,778.93</td>\n",
       "      <td>$6,288.95</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$142,067.87</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>$142,067.87</td>\n",
       "      <td>$7,103.39</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$159,171.27</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>$159,171.27</td>\n",
       "      <td>$7,958.56</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$177,129.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>$177,129.83</td>\n",
       "      <td>$8,856.49</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$195,986.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>$195,986.32</td>\n",
       "      <td>$9,799.32</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$215,785.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>$215,785.64</td>\n",
       "      <td>$10,789.28</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$236,574.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>$236,574.92</td>\n",
       "      <td>$11,828.75</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$258,403.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>$258,403.66</td>\n",
       "      <td>$12,920.18</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$281,323.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>$281,323.85</td>\n",
       "      <td>$14,066.19</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$305,390.04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>$305,390.04</td>\n",
       "      <td>$15,269.50</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$330,659.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>$330,659.54</td>\n",
       "      <td>$16,532.98</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$357,192.52</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>$357,192.52</td>\n",
       "      <td>$17,859.63</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$385,052.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>$385,052.14</td>\n",
       "      <td>$19,252.61</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$414,304.75</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>$414,304.75</td>\n",
       "      <td>$20,715.24</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$445,019.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>$445,019.99</td>\n",
       "      <td>$22,251.00</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$477,270.99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>$477,270.99</td>\n",
       "      <td>$23,863.55</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$511,134.54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>$511,134.54</td>\n",
       "      <td>$25,556.73</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$546,691.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>$546,691.26</td>\n",
       "      <td>$27,334.56</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$584,025.83</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>$584,025.83</td>\n",
       "      <td>$29,201.29</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$623,227.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>$623,227.12</td>\n",
       "      <td>$31,161.36</td>\n",
       "      <td>$10,000.00</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$664,388.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>$664,388.48</td>\n",
       "      <td>$33,219.42</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$597,607.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>$597,607.90</td>\n",
       "      <td>$29,880.39</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$527,488.29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>$527,488.29</td>\n",
       "      <td>$26,374.41</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$453,862.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>$453,862.71</td>\n",
       "      <td>$22,693.14</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$376,555.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>$376,555.84</td>\n",
       "      <td>$18,827.79</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$295,383.64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>$295,383.64</td>\n",
       "      <td>$14,769.18</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$210,152.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>$210,152.82</td>\n",
       "      <td>$10,507.64</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$120,660.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>$120,660.46</td>\n",
       "      <td>$6,033.02</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$26,693.48</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>$26,693.48</td>\n",
       "      <td>$1,334.67</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$-71,971.84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>$-71,971.84</td>\n",
       "      <td>$-3,598.59</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$-175,570.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>$-175,570.44</td>\n",
       "      <td>$-8,778.52</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$-284,348.96</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>$-284,348.96</td>\n",
       "      <td>$-14,217.45</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$-398,566.41</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>$-398,566.41</td>\n",
       "      <td>$-19,928.32</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$-518,494.73</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>$-518,494.73</td>\n",
       "      <td>$-25,924.74</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$-644,419.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>$-644,419.46</td>\n",
       "      <td>$-32,220.97</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$-776,640.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>$-776,640.44</td>\n",
       "      <td>$-38,832.02</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$-915,472.46</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>$-915,472.46</td>\n",
       "      <td>$-45,773.62</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$-1,061,246.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>$-1,061,246.08</td>\n",
       "      <td>$-53,062.30</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$-1,214,308.38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>$-1,214,308.38</td>\n",
       "      <td>$-60,715.42</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$-1,375,023.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50</th>\n",
       "      <td>$-1,375,023.80</td>\n",
       "      <td>$-68,751.19</td>\n",
       "      <td>$0.00</td>\n",
       "      <td>$-100,000.00</td>\n",
       "      <td>$-1,543,774.99</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           begbal     capgain    deposit     withdraw         endbal\n",
       "1           $0.00       $0.00 $10,000.00        $0.00     $10,000.00\n",
       "2      $10,000.00     $500.00 $10,000.00        $0.00     $20,500.00\n",
       "3      $20,500.00   $1,025.00 $10,000.00        $0.00     $31,525.00\n",
       "4      $31,525.00   $1,576.25 $10,000.00        $0.00     $43,101.25\n",
       "5      $43,101.25   $2,155.06 $10,000.00        $0.00     $55,256.31\n",
       "6      $55,256.31   $2,762.82 $10,000.00        $0.00     $68,019.13\n",
       "7      $68,019.13   $3,400.96 $10,000.00        $0.00     $81,420.08\n",
       "8      $81,420.08   $4,071.00 $10,000.00        $0.00     $95,491.09\n",
       "9      $95,491.09   $4,774.55 $10,000.00        $0.00    $110,265.64\n",
       "10    $110,265.64   $5,513.28 $10,000.00        $0.00    $125,778.93\n",
       "11    $125,778.93   $6,288.95 $10,000.00        $0.00    $142,067.87\n",
       "12    $142,067.87   $7,103.39 $10,000.00        $0.00    $159,171.27\n",
       "13    $159,171.27   $7,958.56 $10,000.00        $0.00    $177,129.83\n",
       "14    $177,129.83   $8,856.49 $10,000.00        $0.00    $195,986.32\n",
       "15    $195,986.32   $9,799.32 $10,000.00        $0.00    $215,785.64\n",
       "16    $215,785.64  $10,789.28 $10,000.00        $0.00    $236,574.92\n",
       "17    $236,574.92  $11,828.75 $10,000.00        $0.00    $258,403.66\n",
       "18    $258,403.66  $12,920.18 $10,000.00        $0.00    $281,323.85\n",
       "19    $281,323.85  $14,066.19 $10,000.00        $0.00    $305,390.04\n",
       "20    $305,390.04  $15,269.50 $10,000.00        $0.00    $330,659.54\n",
       "21    $330,659.54  $16,532.98 $10,000.00        $0.00    $357,192.52\n",
       "22    $357,192.52  $17,859.63 $10,000.00        $0.00    $385,052.14\n",
       "23    $385,052.14  $19,252.61 $10,000.00        $0.00    $414,304.75\n",
       "24    $414,304.75  $20,715.24 $10,000.00        $0.00    $445,019.99\n",
       "25    $445,019.99  $22,251.00 $10,000.00        $0.00    $477,270.99\n",
       "26    $477,270.99  $23,863.55 $10,000.00        $0.00    $511,134.54\n",
       "27    $511,134.54  $25,556.73 $10,000.00        $0.00    $546,691.26\n",
       "28    $546,691.26  $27,334.56 $10,000.00        $0.00    $584,025.83\n",
       "29    $584,025.83  $29,201.29 $10,000.00        $0.00    $623,227.12\n",
       "30    $623,227.12  $31,161.36 $10,000.00        $0.00    $664,388.48\n",
       "31    $664,388.48  $33,219.42      $0.00 $-100,000.00    $597,607.90\n",
       "32    $597,607.90  $29,880.39      $0.00 $-100,000.00    $527,488.29\n",
       "33    $527,488.29  $26,374.41      $0.00 $-100,000.00    $453,862.71\n",
       "34    $453,862.71  $22,693.14      $0.00 $-100,000.00    $376,555.84\n",
       "35    $376,555.84  $18,827.79      $0.00 $-100,000.00    $295,383.64\n",
       "36    $295,383.64  $14,769.18      $0.00 $-100,000.00    $210,152.82\n",
       "37    $210,152.82  $10,507.64      $0.00 $-100,000.00    $120,660.46\n",
       "38    $120,660.46   $6,033.02      $0.00 $-100,000.00     $26,693.48\n",
       "39     $26,693.48   $1,334.67      $0.00 $-100,000.00    $-71,971.84\n",
       "40    $-71,971.84  $-3,598.59      $0.00 $-100,000.00   $-175,570.44\n",
       "41   $-175,570.44  $-8,778.52      $0.00 $-100,000.00   $-284,348.96\n",
       "42   $-284,348.96 $-14,217.45      $0.00 $-100,000.00   $-398,566.41\n",
       "43   $-398,566.41 $-19,928.32      $0.00 $-100,000.00   $-518,494.73\n",
       "44   $-518,494.73 $-25,924.74      $0.00 $-100,000.00   $-644,419.46\n",
       "45   $-644,419.46 $-32,220.97      $0.00 $-100,000.00   $-776,640.44\n",
       "46   $-776,640.44 $-38,832.02      $0.00 $-100,000.00   $-915,472.46\n",
       "47   $-915,472.46 $-45,773.62      $0.00 $-100,000.00 $-1,061,246.08\n",
       "48 $-1,061,246.08 $-53,062.30      $0.00 $-100,000.00 $-1,214,308.38\n",
       "49 $-1,214,308.38 $-60,715.42      $0.00 $-100,000.00 $-1,375,023.80\n",
       "50 $-1,375,023.80 $-68,751.19      $0.00 $-100,000.00 $-1,543,774.99"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Let's set up a bank account to make sure we are getting a zero ending balance\n",
    "\n",
    "acct = pd.DataFrame(dtype=float,columns=['begbal','capgain','deposit','withdraw','endbal'],index=np.arange(1,N_SAVING + N_WITHDRAW + 1))\n",
    "acct.deposit = np.where(acct.index <= N_SAVING, PMT,0)\n",
    "acct.withdraw= np.where(acct.index > N_SAVING, -WITHDRAWAL,0)\n",
    "for t in acct.index:\n",
    "    if t==1:\n",
    "        acct.loc[t,'begbal'] = PV\n",
    "    else:\n",
    "        acct.loc[t,'begbal'] = acct.loc[t-1,'endbal']\n",
    "    acct.loc[t,'capgain'] = acct.loc[t,'begbal']*RATE\n",
    "    acct.loc[t,'endbal']  = acct.loc[t,'begbal'] + acct.loc[t,'capgain'] + acct.loc[t,'deposit'] + acct.loc[t,'withdraw']\n",
    "acct"
   ]
  }
 ],
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