presentation_annuity_loans.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Author: Ph.D. Velibor Zeli\n",
    "\n",
    "This document is released under a common license, allowing for broad usage and distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mathematics Behind Annuity Loans (Swe., annuitetslån)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 1A\n",
    "    \n",
    "Jim wants to borrow $P_1$ from the bank. He takes an annuity loan with monthly interest rate of $r$ and agrees to make 3 payments $A$ so that he repays the loan in 3 months."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Payment schedule:\n",
    "\n",
    "|  Month  | Principal | Interest    |  Amortization |  Outstanding principal |\n",
    "|---------|-----------|-------------|---------------|------------------------|\n",
    "|    1    | $P_1$     | $P_1 \\, r$  |    A          | $P_2 = P_1 \\, (1+r)-A$ |\n",
    "|    2    | $P_2$     | $P_2 \\, r$  |    A          | $P_3 = P_2 \\, (1+r)-A$ |\n",
    "|    3    | $P_3$     | $P_3 \\, r$  |    A          | $P_4 = P_3 \\, (1+r)-A$ |\n",
    "|    4    | $P_4 = 0$ |    -        |    -          | -                      |\n",
    "\n",
    "where $P_1 \\gt P_2 \\gt P_3 \\gt P_4$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Derivation:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the first month Jim owes the interest on the initial principal $P_1 r$ and makes a payment $A$ which covers the interest and, the leftover, reduces the outstanding principal. The outstanding principal $P_2$ is than\n",
    "    \n",
    "$$\n",
    "\\begin{align}\n",
    "P_2 &= P_1 - (A - P_1 \\, r) \\notag \\\\\n",
    "&= P_1 \\, (1+r) - A. \\notag\n",
    "\\end{align}\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the second month Jim owns the interest $P_2 r$ on the outstanding principal $P_2$ and makes another payment $A$. This further reduces his outstanding principal to\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "P_3 &= P_2 - (A - P_2 \\, r) \\notag \\\\\n",
    "&= P_2 \\, (1+r) - A \\notag \\\\\n",
    "& = \\left(P_1 \\, (1+r) - A\\right)(1+r) - A. \\notag\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, after the third month Jim makes the last payment $A$ and pays off the interest on the remaining principal and settles the loan\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "P_4 &= P_3 - (A - P_3 \\, r) \\notag \\\\\n",
    "&= P_3 \\, (1+r) - A \\notag \\\\\n",
    "&= (\\left(P_1 \\, (1+r) - A\\right)(1+r) - A)(1+r)-A. \\notag\n",
    "\\end{align}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After the final payment the loan is settled and therefore $P_4 = 0$. Solving the above equation for $A$ using the geometric progression series gives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$ A = P \\frac{r}{1 - \\left( \\frac{1}{1 + r} \\right)^T}, \\qquad (1)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where the symbols denote\n",
    "\n",
    "* monthly payment $A$\n",
    "* loan principal $P$\n",
    "* monthly interest rate $r$\n",
    "* loan term $T$ in months."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Do not follow the derivation on [Wikipedia](ttps://en.wikipedia.org/wiki/Amortization_calculator) because it is wrong (consider this as an anti-reference)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 1B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a scenario in which Jim borrows 1 000 SEK and promisses to repay it in three months with 0.25% monthly interest rate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameters:\n",
    "\n",
    "* `p1 = 1_000`\n",
    "* `r = 0.0025`\n",
    "* `T = 3`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "p1, r, T = 1_000, 0.0025, 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Monthly payment: 335.00 SEK\n"
     ]
    }
   ],
   "source": [
    "A = p1 * r / ( 1 - ( 1 / ( 1 + r))**T)\n",
    "\n",
    "print(f\"Monthly payment: {A:.2f} SEK\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Initial principle: 1,000.00 SEK\n"
     ]
    }
   ],
   "source": [
    "print(f\"Initial principle: {p1:,.2f} SEK\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Principle after the first payment: 667.50 SEK\n"
     ]
    }
   ],
   "source": [
    "p2 = (p1*(1+r)-A)\n",
    "\n",
    "print(f\"Principle after the first payment: {p2:,.2f} SEK\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Principle after the second payment: 334.17 SEK\n"
     ]
    }
   ],
   "source": [
    "p3 = (p1*(1+r) - A)*(1+r) - A\n",
    "\n",
    "print(f\"Principle after the second payment: {p3:,.2f} SEK\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Principle after the third payment: -0.00 SEK\n"
     ]
    }
   ],
   "source": [
    "p4 = ((p1*(1+r) - A)*(1+r) - A)*(1+r) - A\n",
    "\n",
    "print(f\"Principle after the third payment: {p4:,.2f} SEK\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 2A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sue wants to borrow 1 000 SEK from the bank with 4% annual interest rate and agrees to repay the loan in 1 year.\n",
    "\n",
    "- What is her monthly payment?\n",
    "- How much money, in total, does she give to the bank after the loan is settled?\n",
    "\n",
    "Parameters:\n",
    "- `p = 1_000`\n",
    "- `r = 0.04`\n",
    "- `T = 1`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from src.annuity_loan_model import get_payment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "p, r, T = 1_000, 0.04, 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = get_payment(p, r, T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Monthly payment: 85.15 SEK\n"
     ]
    }
   ],
   "source": [
    "print(f\"Monthly payment: {A:.2f} SEK\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total: 1021.80 SEK (102.18% of P)\n"
     ]
    }
   ],
   "source": [
    "print(f\"Total: {12 * T * A:.2f} SEK ({12 * T * A/p:.2%} of P)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The net profit ($\\eta$) on the loan is\n",
    "\n",
    "$$\\eta = \\frac{1,021.80-1,000.00}{1,000.00} = 2.18\\% ,$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and is **less than the annual interest rate 4.00%, on which Sue borrowed, because Sue held the loan for one year and the outstanding principal is a strictly decreasing function of time.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 2B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How does the same scenario look like if Sue borrowed the money for 10 years?\n",
    "\n",
    "Parameters:\n",
    "- `P = 1_000`\n",
    "- `r = 0.04`\n",
    "- `T = 10`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "p, r, T = 1_000, 0.04, 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = get_payment(p, r, T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Monthly payment: 10.12 SEK\n"
     ]
    }
   ],
   "source": [
    "print(f\"Monthly payment: {A:.2f} SEK\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Total: 1214.94 SEK (121.49% of P)\n"
     ]
    }
   ],
   "source": [
    "print(f\"Total: {12 * T * A:.2f} SEK ({12 * T * A/p:.2%} of P)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The net profit ($\\eta$) on the loan is\n",
    "\n",
    "$$\\eta = \\frac{1,214.94-1,000.00}{1,000.00} = 21.49\\% .$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this scenario, **the monthly payments are lower than in the previous scenario but the net profit for the bank is much higher since Sue decided to hold the loan for longer.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dynamics of Annuity Loans"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Annuity loans are payed off with monthly payments $A$ that compose of\n",
    "\n",
    "- interest payments $ I_n $\n",
    "- principal repayment $ A_n^\\prime $ - part that reduces the outstanding principal\n",
    "\n",
    "Therefore, we can write\n",
    "\n",
    "$$ A = I_n + A_n^\\prime .$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 3A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider a millennial Svensson family that wants to take on a mortgage and borrow 2 500 000 SEK for 30 years assuming that the family gets 4.5% interest rate.\n",
    "\n",
    "* How does the outstanding principle decrease with time?\n",
    "* How much interest is payed for the loan in total after the loan is settled?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameters:\n",
    "- `P = 2_500_000`\n",
    "- `r = 0.045`\n",
    "- `T = 30`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "p, r, T = 2_500_000, 0.045, 30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = get_payment(p, r, T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Monthly payment: 12,700 SEK\n"
     ]
    }
   ],
   "source": [
    "print(f\"Monthly payment: {round(A,-2):,.0f} SEK\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualization:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from src.plotting import plot_loan_dynamics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Principal: 2,500,000 SEK; Interest rate: 4.50%; Term: 30 Y => 82.41%\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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bY4qQtLQ0ypQpQ82aNZE8rjq/a9cuypQ57O2ri4RwbouqsmXLFtLS0qhVq1ahyipowIjCu+tWa6AFMFFETtYg/gtQVVXyuJF5LvFupD4YIDExkZSUlGC9daGkp6eHTV0Ko7i0A6wtoRIfH0+FChVIT0/Pc352dja7duV5i5QiJ9zbEh0dzfbt2wu97RQ0YKQBH7kAMUdEcvBuarLJJ89a/uleAu+qkSkuvZpfeu716TeISGVVXScilfEuEpgnVR0NjAZISkrScBnSVlSH1/krLu0Aa0uoLF26lLJl/e+j9Y9w/lV+pIpCW2JjY2nWrFmhyijosNpPgI4AIlIP7zLSm0Wkqojk3gDkK6CLu19CAtAF+Mp1Oe0UkdZudNQAvGvhg3d999zRVAN90o0xxoTYYY8wRGQ83pFCRRFJwxv5NAYY44baZgIDXRdSZbz7J6CqW0XkEbxr/4N3j9+t7vX1eKOvSuKd7P7CpT+O1701CO9Win0L3UJjTFiYP//g6d27IyjMn6NPP/3weUqXLp1vl1iukSNHMnjwYEqVKlXwyhzGJ598Qr169WjUqNFRe49jIZBRUvndS+CyPNJaAy/6LDsGL7j4lzmPPG7Bqd5d4Dofrk7GGBMsI0eO5LLLLjuigJGdnU1kZGTA+T/55BN69OhR5ANGUP/praovqOqUYJZpjDGFlXvup3fv3jRo0IBLL70UVWXUqFH8/fffdOzYkY4dOwLw9ddf06ZNG5o3b06fPn0OHKHUrFmTe+65h+bNm/PBBx8clG/AgAEH8t177700atSIU089lTvvvJNZs2YxZcoU7rrrLpo2bcoff/wRss+hsIrFtaSMMeZwfv75Z5YsWUKVKlVo164dM2fO5Oabb2bEiBHMmDGDihUrsnnzZoYNG8Y333xDXFwcTzzxBCNGjOCBBx4AoEKFCixYsIDNmzfTq1evA/kefvhhRowYwQ033MDHH3/MsmXLEBG2b99OuXLlOP/88+nRowe9e/cO8adQOBYwjDHHhZYtW1KtmjdAs2nTpqxatYr27dsflGf27Nn89ttvtGvXDoDMzEzatGlzYP7FF1+cZ769e/fSrl074uPjiY2NZdCgQfTo0YMePXoci6YdMxYwjDHHhZiYmAOvIyMjycrK+lceVeXss89m/PjxeZaRewlz/3y+w2rnzJnD9OnTmTRpEi+88ALffvttsJsSMna1WmPMca1MmTIH/nTXunVrZs6cSWpqKuDd52L58uX/Wia/fOnp6ezYsYPu3bvz7LPP8ssvv/zrPYoyO8IwxhwT/sNgd+3KIRz+6zZ48GC6detGlSpVmDFjBmPHjqV///7s27cPgGHDhlGvXr2DlqlUqdJB+XJycnj00UcpU6YMPXv2ZO/evagqI0aMAKBfv35cc801jBo1ikmTJlG7du1j3s5gKBb39E5KSlK7gVJwFZd2gLUlVJYuXUrDhg3znV8U/h0dqKLQlrzWh4jMV9WkQMuwLiljjDEBsYBhjDEmIBYwjDHGBMQChjHGmIBYwDDGGBMQCxjGGGMCYv/DMMYcE79tPviPa5n79hG9r+DlNaoY2DDWTz75hAsvvJClS5fSoEGDgr9hPlJSUsjKyuKss84C4JVXXqFUqVIMGDDgiMuJjo6mbdu2hSrnaLKAYYwp1saPH0/79u0ZP348Dz30UFDLzsrKIiUlhRIlShwIGEOGDClQWSkpKZQuXfpAwChoOUeTBQxjTLGVnp7ODz/8wIwZMzjvvPN46KGHSElJ4cEHH6RcuXIsXryYvn370qRJE5577jkyMjL45JNPqF27NqtWreKqq65i8+bNVKpUiTfffJMaNWpwxRVXEBsby88//0zVqlWZNWsWERERfPDBBzz//PNMnz6d0qVLc8kll9C9e/cDdVm8eDErV65k0aJFDBs2jMzMTCpUqMC7775LRkYGr7zyCpGRkbzzzjsHlXPnnXeycOFChgwZwp49e6hduzZjxowhISGB5ORkWrVqxYwZM9i+fTtvvPEGHTp0OGqfp53DMMYUW5MnT6Zbt27Uq1ePChUqMN/d9u+XX37hlVdeYenSpbz99tssX76cOXPmcPXVV/P8888DcNNNNzFw4EAWLVrEpZdeys0333yg3LS0NGbNmsVHH33EkCFDuOGGG1i4cOFBX9ZVqlRh4cKFLFy4kGuuuYaLLrqIk046ifbt2zN79mx+/vln+vXrx5NPPknNmjUZMmQIt91227/KARgwYABPPPEEixYtokmTJgcdKWVlZTFnzhxGjhwZ9CMofxYwjDHF1vjx4+nXrx/gXc8p9+qyLVq0oHLlysTExFC7dm26dOkCQJMmTVi1ahUAP/74I5dccgkAl19+OT/88MOBcvv06RPwHfdmzpzJa6+9xpgx3s1H09LS6Nq1K02aNOGpp55iyZIlh1x+x44dbN++nTPPPBOAgQMH8t133x2Y36tXLwBOP/30A3U/Wg4bMERkjIhsdPfv9p93h4ioiFTMZ9n7RCRVRH4Xka4+6d1cWqqI3OuTXktEfnLp74tIdEEbZow5vm3dupVvv/2Wq6++mpo1a/LUU08xceJEVPWgS51HREQcmI6IiMjzsuf+4gK8Gfm6desYNGgQEydOpHTp0oB35HLjjTeyePFiXn31Vfbu3VuA1v0jt+75XbI9mAI5whgLdPNPFJHqQBdgdV4LiUgjoB/Q2C3/kohEikgk3n2/zwEaAf1dXoAngGdVtQ6wDRh0RK0xxhhn0qRJXH755fz111+sWrWKNWvWUKtWLb7//vuAlm/bti0TJkwA4N1338333EB+ly7fv38/ffr04Yknnjjoarc7duygatWqAIwbN+6w5cTHx5OQkHCg3m+//faBo41j7bAnvVX1OxGpmcesZ4G7gcn5LNoTmKCq+4A/RSQVaOnmparqSgARmQD0FJGlQCfgEpdnHDAUeDmwphhjwpn/MNhduziqV3gdP34899xzz0FpF110ES+//HJAlxd//vnnufLKK3nqqacOnPTOy3nnnUevXr348ssvD5z/AJg1axbz5s3jwQcf5MEHHwRg6tSpDB06lD59+pCQkECnTp34888/D5TTu3dvJk+efFA54AWW3JPeJ598cr51OdoCury5Cxifqeopbron0ElVbxGRVUCSqm72W+YFYLaqvuOm3wC+cLO7qerVLv1yoBVecJjtji5yj2C+yH3PPOo0GBgMkJiYeHruL4FQS09PP3DoWZQVl3aAtSVU4uPjqVOnTr7zs7OzAz4PEO6KQltSU1PZsWPHQWkdO3Y8osubH/GwWhEpBdyP1x0VMqo6GhgN3v0wwuUeAUXpfgWHUlzaAdaWUFm6dOkhjyCKwj0kAlUU2hIbG0uzZs0KVUZBRknVBmoBv7iji2rAAhE50S/fWqC6z3Q1l5Zf+hagnIhE+aUbY4wJA0ccMFR1saqeoKo1VbUmkAY0V9X1ItJSRN5yWacA/UQkRkRqAXWBOcBcoK4bERWNd2J8inp9YzOA3m75geR/fsQYUwQUhzt6FgfBWg+BDKsdD/wI1BeRNBE51MilGkCGq+ASYCLwG/AlcIOqZqtqFnAj8BWwFJjo8gLcA9zuTpBXAN4oWLOMMaEWGxvLli1bLGiEmKqyZcsWYmNjC11WIKOk+h9mfk2fyVZ4Q2Zz5w0HhuexzFRgah7pK/lnJJUxpgirVq0aaWlpbNq0Kc/5e/fuDcqXWDgI97bExsZSrVq1QpcT1GtJqepdwSzPGFN0lShRglq1auU7PyUlpdAnYcNFcWrLodilQYwxxgTEAoYxxpiAWMAwxhgTEAsYxhhjAmIBwxhjTEAsYBhjjAmIBQxjjDEBsYBhjDEmIBYwjDHGBMQChjHGmIAE9dIgRc2tt97KvAU/E8xLo6Xv3EHpsvFBLDE0iks7wNoSrqwthXdKk1N5ftRzREcem9/+x3XAANiblR3UgKGq7M3KDmKJoVFc2gHWlnBlbSm87fv2s3t/FtGR0cfk/Y7rgDFy5EgWrN9OTGQEIhKUMlcvnEuNpi2CUlYoFZd2gLUlXFlbCm/P/mMbpOwchjHGmIBYwDDGGBMQCxjGGGMCEsgtWseIyEYR+dUn7SkRWSYii0TkYxEpl8+yA0VkhXsM9Ek/XUQWi0iqiIwSdwJBRMqLyDSXf5qIJAShjcYYY4IgkCOMsUA3v7RpwCmqeiqwHLjPfyERKQ88iHfb1pbAgz4B4GXgGqCue+SWfy8wXVXrAtPdtDHGmDBw2IChqt8BW/3SvlbVLDc5G8jrZrFdgWmqulVVt+EFmW4iUhkoq6qz1bs7/FvABW6ZnsA493qcT7oxxpgQC8aw2quA9/NIrwqs8ZlOc2lV3Wv/dIBEVV3nXq8HEvN7UxEZDAwGSExMJCUlpSB1Z09WNhEEZ0gtQGbGblYvnBu08kKluLQDrC3hytpSeDmq7IiKIDJIfws4nEIFDBH5D5AFvBuc6vxDVVVE8v1PnaqOBkYDJCUlaXJycoHex/6Hkbfi0g6wtoQra0vh7dmfTe2EUiTEHps/7hV4lJSIXAH0AC51XUv+1gLVfaarubS1HNyFlZsOsMF1WeGeNxa0fsYYY4KrQAFDRLoBdwPnq+oen/SqIjLdTX4FdBGRBHeyuwvwlety2ikird3oqAHAZLfMFCB3NNVAn3RjjDEhdtguKREZDyQDFUUkDW/k031ADDDNdeXMVtUhQGW8LipUdauIPALkduw9rKq5J8+vxxt9VRL4wj0AHgcmisgg4C+gbyHbZ4wxJkgOGzBUtX8eyW/kk7018KLPsmOAMXmUOQ84JY/0LUDnw9XJGGPMsRfUiw+q6gvBLM8YY0z4sEuDGGOMCYgFDGOMMQGxgGGMMSYgFjCMMcYExAKGMcaYgFjAMMYYExALGMYYYwJiAcMYY0xALGAYY4wJiAUMY4wxAbGAYYwxJiAWMIwxxgTEAoYxxpiAWMAwxhgTEAsYxhhjAmIBwxhjTEAsYBhjjAnIYQOGiIwRkY0i8qtPWnkRmSYiK9xzQj7L3iciqSLyu4h09Unv5tJSReRen/RaIvKTS39fRKIL20BjjDHBEcgRxligm1/avcB0Va0LTHfTBxGRRkA/oLFb/iURiRSRSLz7fp8DNAL6u7wATwDPqmodYBsw6IhbZIwx5qg4bMBQ1e+ArX7JPYFx7vU44II8Fu0JTFDVfar6J5AKtHSPVFVdqaqZwASgp4gI0AmYdJhyjTHGhEBUAZdLVNV17vV6IDGPPFWB2T7TaS4NYI1feiugArBdVbPyyP8vIjIYGAyQmJhISkrKETbBsycrmwikQMvmJTNjN6sXzg1aeaFSXNoB1pZwZW0pvBxVdkRFECnB+w47lIIGjANUVUVEg1GZI3zf0cBogKSkJE1OTi5QOQvWbycmMgIJ0ge+euFcajRtEZSyQqm4tAOsLeHK2lJ4e/ZnUzuhFAmxx+Z0b0FHSW0QkcoA7nljHnnWAtV9pqu5tPzStwDlRCTKL90YY0wYKGjAmAIMdK8HApMBRKSliLzlk6efiMSISC2gLjAHmAvUdSOiovFOjE9RVQVmAL39yzXGGBN6gQyrHQ/8CNQXkTQRGQQ8DpwtIiuAs9w0QA0gA0BVlwATgd+AL4EbVDXbnaO4EfgKWApMdHkB7gFuF5FUvHMabwSnmcYYYwrrsOcwVLV/PrM655HWCm/IbO6yw4HheZQ5FZiaR/pKvFFUxhhjwkyhT3r7UtW7glmeMcaY8BHUgFEUDb/rVqpUrUbj05rS8NSmVErMa4SwMcaY4zpg7N27lznfzyTtr9QDaRVPOJFGpzWl8Wmn0ejUpjQ6rSmJlasEbditMcYUVcd1wIiNjWXM68vJzNnOst8Xsmz5PFJTF7By+UJ+mP41OTk5AFx96z3cfO/97M/cy+zvU2jWsjXx5fK8fJYxxhRbx3XAABCEExISOLFtR5LbdgS8f09u35nOkmVeEKlzSlNWrs4hdelC7hx4MY++8i5ndT+XNX8s5X9fT6Vx02Y0Pq0ZCRUqhLg1xhhz9Bz3ASMvESKUjy9Dh1Yd6NCqA+AFkbjqbXl61LdUrdaQdWsi+PabObz42CMHlqtSvQYn16xJ685dOLV5Eg1PPY1ScXGhaoYxxgSVBYwARYiQULb0gaMQgIEX3ET3My7j19/ms+z3uSxfMZ/lv87ih++/AyAyMpLa9Rvx+qRPqFCpEum7dlKyVByRkZGhaoYxxhSYBYxCiBAhsUJ5EjucTecOZwOwYUMK+3Lq88vi2Sz7/SdW/fkrW3eXIyM7m+cevpeFs79n6pxfKBEVwR/LfyexcmVKlykb4pYYY8zhWcA4CmpUrkyNyhdyXpcLAcjMyiFjew5JzS6kerVmrFoDUSWyuGnA5axe+Tt1GjSiWctWNGvZiqYtWlG9Zi0blWWMCTsWMI6B6KgIoqMiOL9LLwAUZW+Gct0NI1m0+AeW/vYjn036gInjxgCQULESTVu0onnLVrRN7kSDU5qEsvrGGANYwAgJQSgZLZx1RlfOOsO7c+2+zCyWrviVhYtm8ttvP7Ls19nM+OIzVq1ay20PPkaJiGxeemIo5/ftbwHEGBMSFjDCREx0FE0bN6Vp46bADSjK3+vXs3tfJtvSovlr7RLee+M1atRLolKNRqT9sYTxr71Ai7btSWrTlhon17ZuLGPMUWUBI0wJQtUTKx+Yrly3Bd9M3076vix2pEXx64I0vvvmGz79YAIAlRIrc3qbtrRs156ktu05uW49CyDGmKCygFGExJWMJa6k97rXWRdzXnIflq5YwrwFKSxe9B0//fADX37yIeCdB0lq3ZahI56jXEL5ENbaGFNcWMAowkpERXBqwyac2rAJXHoT2Tk5rFi5gjnzZrB48XcsX/YLW9NLs0+zGTvqEbasX8uTr7wW6mobY4ooCxjFSGREBA3q1KdBnfrQbwg5qmTszSF9Rxb7M2LJzIph1dpsYmPhzoE9KF06jpbtO9Cqwxk0OOVU+0OhMeaQLGAUYxEixEVHEhcdyR3XD0dR9uzOYdfWTE6s3JDFC7/j++lfA1C2XAIt23WgbXJHWnc4E1RDXHtjTLgpVMAQkduAqwEFFgNXqupen/nlgfeBmsAqoK+qbhPvbOxzQHdgD3CFqi5wywwE/uuKGKaq4wpTR/MPQYiLiSQupiSP/Pc1clRJW7eWmbO/YeHCb1k4bwbffD4FgEonnMAt/32YC/tfEuJaG2PCxWHv6Z0fEakK3AwkqeopQCTQzy/bvcB0Va0LTHfTAOcAdd1jMPCyK7M88CDerV5bAg+KiF1H/CiJEKFGlWr073UFTzz8Fp9/+hdvvfcb1986itp16rM3K54167OZ/eNCenZozeIF80NdZWNMCBW2SyoKKCki+4FSwN9+83sCye71OCAFuMelv6WqCswWkXIiUtnlnaaqWwFEZBrQDRhfyHqaAERGRNCoXkMa1WvIuWc3oWKlM0nfns22NKVU6RPIyK7E35uy+frjsUybPJG2ZybT+oxkTj09iRIlSoS6+saYo0y0EH3VInILMBzIAL5W1Uv95m9X1XLutQDbVLWciHwGPK6qP7h50/ECSTIQq6rDXPr/ARmq+nQe7z0Y7+iExMTE0ydMmFCgNuzaBcE815uVlU5UVOngFRgiebVD1bvM+4yUaXw25SNSU5ejqpQsWZLTmjbj9KQkTm/RgsqVq4So1nnLzNhNdMnicZl5a0t4ClVbclSJiYogsoD/uerYseN8VU0KNH+BjzBcV1FPoBawHfhARC5T1Xfyyq+qKiJBO5OqqqOB0QBJSUmanJxcoHK++Qbi4yGiwJ1zB9uwIYXExILVJZwcqh2X9u/IJf2Hs3HzFmbNmc78+dNYMGcas3+cBUCNWrU569we3PHgI3kuf6ytXjiXGk1bhLoaQWFtCU+hasue/dnUTihFQmz0MXm/wnRJnQX8qaqbAETkI6At4BswNohIZVVd57qcNrr0tUB1n3zVXNpa/unCyk1PKUQdzVEiCIkVK3Jh94u5sPvFZOfksGzFMmbO/pL5875i2dI/Wbcpm5Il4aVH/0Or9u3p3L1HqKttjCmEwgSM1UBrESmF1yXVGZgnIo8Bc1T1Y2AKMBB43D1PdstOAW4UkQl4J7h3uKDyFfCoz4nuLsB9haijOUYiIyJoXL8Rjes3goG3s29/NumbcliXuYtvv/iSiOgEmrTphmTv4e0Xn+aMs7vStGUroqJsZLcxRUWB91ZV/UlEJgELgCzgZ7wuog/xAgJ4gWKiiAwC/gL6uvSpeENqU/GG1V7pytwqIo8Ac12+h3NPgJuiJaZEJDElIqkQV55PPlrBroxMdv8Ni5bMYezLL/DGCyMpUzaeth0707FrN9p3OtvuiW5MmCvUzztVfRBvGOwBIlJCVX9087fgHXn4L6fADfmUOQYYU5h6mfASGRFBubhYAE5s1ZWkrzby3cyv+HH258z+/iu+mvwRIkKT5i04s0sXzjy7Gw1OaWIXTzQmzATpVO8/VLVrsMs0xUv5cglccG4/nnjkbb76Yh0vjZ5FvwH3s2fPfp5/bBi9O7Xnj5Vp5OQo6/9eS8aePaGusjEGuzSICbGoyEhaNm9Dy+ZtgGGsXf83P83/DsmqwZ9rsnj87jtIW7WCT2fOIypK2Ld3LzGxsaGutjHHJQsYJqxUPbEKvc71LhiQla1ceP5tbNq+jj/XKNExWQzocho1ataic/dz6dy9B9Vr1gpxjY05fgS9S8qYYImKFDq2P4u+PS6nipRFN0bRuesVbNm8g6ce/A/dWpzG+e1bM+rRR1i6eBGF+ROqMebwLGCYIiFChMSEstx186NMen8x4ycu5+obnqBkqfK89twz9O7Unm4tmjLioQdYu/qvUFfXmGLJuqRMkSMIdU+uS92T72bIlXezbuMGvv72I77/bhJvvvw8zc7sQZmK1dm4ZgV70ncSH2FHHsYEgx1hmCKv8gmJDOx3Ha+/NJ2pU9dzcqX2bFoTycsjXuSqXj3J2LuP7Gxl4/p15OTkhLq6xhRZdoRhipWKFSq6VzHcdt0IOidfRmSE8OeaHG699EJ27dhGlx7n0/X8C2jWqrXdZdCYI2BHGKbYqpCQQMe2nSkhEZyQXZa+fe+hTv0kJr0zjoE9zyH5lPo8dOdtzP7+f2RlZYW6usaEPTvCMMeFElER9LlgAH0uGMCOnTv55n+f8r//TeKTCe8xcdwbJFSoSJfzenLJoMHUadAw1NU1JixZwDDHnfiyZbnovEu56LxL2ZWezvTvPiclZSIfj3+PU1p05oQa9dmzbR1bN2+i4amn2SVKjHEsYJjjWpnSpbmg+8Vc0P1itu/cRUZOBBvXKO+NHcMHY57hs7nLqFEtkb17MyhZqlSoq2tMSFnAMMYpV7YM5dzrK/rcRf1ardm/90RWrc1m6E392bVjC+f17kuPi/pS6cQTQ1lVY0LCTnobk4dKFSpxftdeVI0pQ7l9ZTn99PPJySnB00P/S6fTGjD44ouY+vEk9mZkhLqqxhwzFjCMOYzYEhFcM+BW3ntrLm+PX8JFl9zJ70uWctfgqzijUR3+79YbmT/7R7s0iSn2LGAYEyBBaFi3Effc+gSfTVnF0yO/plX785n60YcMOK8r77/9Hjk5aoHDFFt2DsOYAoiKjCS5/dkktz+bnbt2MXXaJBo2PItVaTlM/3QM/5s6iZfee5+y8eVCXVVjgqZQRxgiUk5EJonIMhFZKiJt/ObHiMj7IpIqIj+JSE2fefe59N9FpKtPejeXlioi9xamfsYcC2XLlKFfryupd0J1ymeWJTIzgdhSldiaXpotO7J5b8wbfD99mv050BR5hT3CeA74UlV7i0g04D/ucBCwTVXriEg/4AngYhFpBPQDGgNVgG9EpJ5b5kXgbCANmCsiU1T1t0LW05hjIqZEBP17XUm/Xlewe3cOW7dmMPrZZ9i0Po2KiZW5sN8l9Lr0cmrUOjnUVTXmiBX4CENE4oEzgDcAVDVTVbf7ZesJjHOvJwGdxfsXVE9ggqruU9U/gVSgpXukqupKVc0EJri8xhQpglA6JpJqZUvz0aQV/N8j71Or9mm88fyznNOyKQN7nsunH7xvo6xMkVKYLqlawCbgTRH5WUReF5E4vzxVgTUAqpoF7AAq+KY7aS4tv3RjiqySsbH0PKcvL4/6go8+WcXlg4ay5q813Hv9NZx5Sj0eufsO/k5bc/iCjAmxwnRJRQHNgZtU9ScReQ64F/i/oNTsMERkMDAYIDExkZSUlAKVk5EBmZnBq1dWVjobNhSsLuGkuLQDwqstJSKhX68z6XtBBxb+spBp06by0bvjSO7QnsxN69i8aSOlS5ehVD7/Ks/M2M3qhXOPca2PDmtL4eWosiMqgshjdPmawgSMNCBNVX9y05PwAoavtUB1IE1EooB4YItPeq5qLo1DpB9EVUcDowGSkpI0OTm5QI345huIj4eIIA0w3rAhhcTEgtUlnBSXdkD4tqVy5U6c0+12tu3Yyf7IGDKjM3nlsf789ccSpv60kBJR/94oVy+cS42mLUJQ2+CzthTenv3Z1E4oRUJs9DF5vwJ/TarqemCNiNR3SZ2B30TkRhG50aVNAQa6172Bb9UbpD4F6OdGUdUC6gJzgLlAXRGp5U6i93N5jSm2EuLLckLpGKpGl+by/vdz2aBh/JWmpG3cx3WX9mPiuDHsTt8V6moaU+g/7t0EvCsii4CmwKNAA7yjCPBOiFcQkVTgdtwRiKouASYCvwFfAjeoarY7z3Ej8BWwFJjo8hpT7AlCy+Zt6XvupSTmxLNhyQ5Wr1zNQ3feypmn1OeB229mxfLloa6mOY4Valitqi4EknzT3H8tbnfz9wJ98ll2ODA8j/SpwNTC1MuYoi4qUmh0cm0mjv+FufN/5KPJr/LpxPf58O2xNHx1NJddPZhzLryImNjYUFfVHEeCfmkQVe3hhsQaYwopQiJoldSOJx55i08/W8vga29i1849/Ofm6+h4agOeeegBMvbsCXU1zXHCriVlTBFRISGBnuf34qMPfuPpkV/TsEk7pn3+BTsySrAvU/lr5R/k5OSEupqmGLNrSRlTxERIxIHrWO3ak8Hu9cLm9du5umcnul7Qm6FPPo1E2F0CTfBZwDCmCCtTqiRlgH2ZCVx307OcULMmf63LZvumVD4b/zqXDx7CSbXrhLqappiwLiljioGY6Bj6XjCQ5KZnEre7LHO+XcgHb73JuW1OZ0j/vsz+LsUuu24KzQKGMcVM6ZhILr/oGj6evIp+A+5j0fx5DLrofC44ow0fvvsW+/buDXUVTRFlAcOYYqpyYhXuuGk4n05Zze33jCYrK4IHbr2RTk0b8fzjw9myaVOoq2iKGAsYxhRzpUqW5JI+1zBx/C8889w06tZvyasjnmTE8EfJyrJuKhM4O+ltzHEiQiI4s91ZnNnuLJanLiUjIopVaTmsWvEjk8Y8x4NPP0vlqtVCXU0TxixgGHMcqlenIQD7s5Qff9/Kn6l/kpEdz+6MHLZtXE3latWJjIwMcS1NuLEuKWOOYyWihN7nXcqk95dSIr0iaauVqy66kO6tT+eDcW+SuW9fqKtowogFDGMMUZERVIyLpmp0GQYNGk5MTFmG3nkLZ59+Km++OMqulmsACxjGGB+REZGc3/1iJryzgKef/YLKVevy9ND/0rlpY557dBjbtmw5fCGm2LKAYYz5FxEhuUM33hz9P155bRaNm3Rg9LNPclazxjx63z12xHGcsoBhjDmkpGZteGHkFN4dv5i2Z1xIyrRv2LEnmsz9SvqunaGunjmGLGAYYwJSv+4pPDn8Hd57ZxH7NpVmRepuurVszsvPPB3qqpljxIbVGmOOSFzJWOKAHTvj6HrOVVSt1Za/N2WTmf432zb9TbOWrUJdRXOU2BGGMaZA4suW5c5bHqNTsy5kbSrJq8++zGXnns2giy7gl3lzQl09cxQUOmCISKSI/Cwin+Uxr7yITBORFe45waWLiIwSkVQRWSQizX2WGejyrxCRgYWtnzHm6IqMECrFxXD7kMcYdN1jLF28iEvOOYur+/Ri0YJ5oa6eCaJgHGHcAizNZ969wHRVrQtMd9MA5wB13WMw8DJ4AQZ4EGgFtAQezA0yxpjwVjquNNcNupfJn6xk0LXD+fXnBfTv2onBF/dm8c/zQ109EwSFChgiUg04F3g9nyw9gXHu9TjgAp/0t9QzGygnIpWBrsA0Vd2qqtuAaUC3wtTRGHNslY4rw3XX3M+nU1Zx5eBhLJo3l35dOnJt/z78mboi1NUzhVDYk94jgbuBMvnMT1TVde71eiDRva4KrPHJl+bS8kv/FxEZjHd0QmJiIikpKUdeeyAjAzIzC7RonrKy0tmwoWB1CSfFpR1gbQml3j3b0f3sZkye8hFTJk9i9eJfkF3byMnOJmf/PlYvnBvqKgZFZsbukLQlR5UdURFEyrG5JW+BA4aI9AA2qup8EUk+XH5VVREJ2rWUVXU0MBogKSlJk5MPW4U8ffMNxMdDRJBO/2/YkEJiYsHqEk6KSzvA2hIObr2lO0OGvEB6VgR7o/fy9AOXEaN7GTX+w1BXLShWL5xLjaYtjvn77tmfTe2EUiTERh+T9yvM12Q74HwRWQVMADqJyDt+eTa4ribc80aXvhao7pOvmkvLL90YU8TFxsRSMS6aypGlqVW9OdWq1+LvTdlk7M3mrz9SQ109E4ACBwxVvU9Vq6lqTaAf8K2qXiYij4nIhS7bFCB3pNNAYLJP+gA3Wqo1sMN1XX0FdBGRBHeyu4tLM8YUE5EREdxy/VD69u7P/o0lmfTuZ/Rom8R9N1zH32lrDl+ACZmj8T+MJnjnKwAeB84WkRXAWW4aYCqwEkgFXgOuB1DVrcAjwFz3eNilGWOKoRNKx9CxeTfOv+gmpn78Ad1bNefx/7uf7VvtIofhKCgBQ1VTVLWHmyyhqj+69C2q2llV66rqWblf/m501A2qWltVm6jqPJ+yxqhqHfd4Mxj1M8aErwrlK/Lfe0bywQfLObNTX94d/RJdTj+VV0Y8xZ7du0NdPeMj6EcYqto12GUaY4q/6tVO4vFhb/HWOwtpfNoZPP/YI3Rr2YwJY99g//79oa6ewS4NYowJMw3qNeGl5z7jpVe+IzHxZB656zbeG/cOmhO0QZamgOzig8aYsNQyqQPjxvzAt//7nNpN27J6fQ6/zvuS8vGlaHNmx1BX77hkAcMYE7ZEhM7JPVCUnTuzefO551CyeOuzM4grGRnq6h13rEvKGBP2BCG+ZBSjX/qW+/7zHn+vjWDJsvXcd+P1rFubFurqHTcsYBhjioySsSVpXLsulSPL8NsPS/jyk0mc2/p0Rj023EZUHQMWMIwxRU5khNDj7AsYP2Eprdr24NURT3BOq+ZMfn88OTk5oa5esWUBwxhTZJ1UvSYjnpzIS698R7mEytx/47X07dKJBT/NDnXViiULGMaYIq9lUgfee2su9/5nDBvWruPyHl247eor7fxGkFnAMMYUCxEREfS+8Eo++vB3LhlwP999/SWpKzeSlWX/3wgWCxjGmGKldFwZbr95OJ9+uoZq5Vvx19ochv3nv3z6wcRQV63Is4BhjCmWEsolcGLpWErvjmHBzNnMn/crO/fkoGpHHAVlf9wzxhRrZeNK8vabP7I1PYMNaTl8++tXfDd1Anc/PIwTq+R5Q0+TDzvCMMYUexEREVQsG0eV6NKsX76BGV9+zrltknht5Agyg3mP5mLOAoYx5rgRIcLA/jcwfvxvNG3eiZHDh9KzQxtmzpge6qoVCRYwjDHHnZNq1OKFkVN44ulP2Z+Zw+C+F3LTwMtY/7fdEfpQLGAYY45bnZN78MH7ixl49UP8MH0a57ZJ4s0XnycrKyvUVQtLBQ4YIlJdRGaIyG8iskREbskjT4yIvC8iqSLyk4jU9Jl3n0v/XUS6+qR3c2mpInJvQetnjDGBiI0pyU1DHmD8+F855bQOjHvlJTZt2W2jqfJQmCOMLOAOVW0EtAZuEJFGfnkGAdtUtQ7wLPAEgMvXD2gMdANeEpFIEYkEXgTOARoB/fMo0xhjgu6kGifz8qipjH59Dunby/Fn2h6eefghu7+4jwIHDFVdp6oL3OtdwFLAf4xaT2Ccez0J6Cwi4tInqOo+Vf0TSAVaukeqqq5U1UxggstrjDFHnYhQ/cQqVImJY/GMnxn70khmzVxAjt3tDwjS/zBcV1Mz4Ce/WVWBNQCqmiUiO4AKLt336mBp/BNs1vilt8rnPQcDgwESExNJSUkpUN0zMiCYo+qystLZsKFgdQknxaUdYG0JV+HeltMalOT1196hfKVyrJw/l5Rvv6ZR40ZUq1b9X3kzM3azeuHcY17HHFV2REUQKXJM3q/QAUNESgMfAreq6s7CVykwqjoaGA2QlJSkycnJBSrnm28gPh4ignT6f8OGFBITC1aXcFJc2gHWlnBVFNqSmOg9r9uyjTFv9GPP7l1cc8udXHPLrUTHxBzIt3rhXGo0bXHM67dnfza1E0qREBt9TN6vUF+TIlICL1i8q6of5ZFlLVDd5Y0C4oEtvulONZeWX7oxxoRM5QoJjH93EW3an89LTw3ngjPbMXfWD6Gu1jFXmFFSArwBLFXVET7pN4rIjW5yCjDQve4NfKve0IMpQD83iqoWUBeYA8wF6opILRGJxjsxPqWgdTTGmGA54YTKjHhyIk8+8xl792RyRc/u3H/T9ezYvi3UVTtmCnOE0Q64HOgkIgvdozvQAO8oAryAUkFEUoHbgXsBVHUJMBH4DfgSuEFVs1U1C7gR+ArvJPpEl9cYY8JCpzPPZdIHv9L3kjv59IPxnNeuFT/Omhnqah0TBT6Hoao/AP860yIi1+MFB1R1L9Ann+WHA8PzSJ8KTC1ovYwx5mgrGRvH3bc/RbcuF/PwI1fy8IMPsCs7kqtvuinUVTuqgv5Pb1Xt4YbEGmNMsXbqKUm89848Lh9wNackXcjGbdmk79pVbP/0Z5cGMcaYQoguEUO/iy+l4Qn12b42imsu7sfd110b6modFXY/DGOMCYLoqAiqlCpJ6xbnElO+LBu2ZlOhrBAZKcgx+p/E0WYBwxhjgiQyMpLBV91DVraycX0GH739KvO+/5xHRo6iSh5/+CtqrEvKGGOCLCpSqBJXipj9cSycM5vz27Vi/JjXycnJCXXVCsUChjHGHCX9+wzmvfcWU69hS4bdczsDe57L6j9XhrpaBWYBwxhjjqIa1Wvx+ivfcMc9r7Bs8WIuTG7H++PeLJIjqSxgGGPMUSYi9O9zLRMmLKZegyQevvMWrrvkYjZv3Bjqqh0RCxjGGHOMVKlcg9df+Zbrbnqa2d/N4M4h1xapS6fbKCljjDmGIiIiGDTwDtq37caOrP2sWZ9NqRK7iI2JoEzZ+FBX75AsYBhjTAjUr9sYRdm6fT9DH7+OFUvmMOX72cSWKhnqquXLAoYxxoSIIFSIi+bSi25hQaO5bNoZzQlRSmRENlFR4ff1bOcwjDEmxJo1bcNV/W9Ct5bi44lf0LNDG35btDDU1foXCxjGGBMGBKFSXDQVoyqyc/tO+nftzBsvjAqrP/tZwDDGmDDSrk1nJoxfRIvW3Rjx0H8ZdNEFbFy/LtTVAixgGGNM2CmfUJFRz07mjrtf5pd5c+jZoTXTPvs01NWygGGMMeFIROjfdwhvvTWfSiecxK1XXsr/3XozGXv2hKxOFjCMMSaM1T65AW+Pm02f/nfw8XvjuGHApSG7rEj4jdsCRKQb8BwQCbyuqo+HuErGGBMy0SViuOeOp2nbugt7SwjrNudQvmwOeozvsxF2AUNEIoEXgbOBNGCuiExR1d9CWzNjjAmtDu26kKPKxo37GP74XUhEJq+9/Pwxe/+wCxhASyBVVVcCiMgEoCdw1AJGRgZEBKlzLifHK6+oKy7tAGtLuLK2FJQQHxlLpTK1qdeyObt3Cwmxx+adwzFgVAXW+EynAa38M4nIYGCwm0wXkd8L9nalYoMXLgAyEyB6W/DKC5Xi0g6wtoQra0uhvShyB3v2QnZ2AUs46Ugyh2PACIiqjgZGh7oe/kRknuq+pFDXo7CKSzvA2hKurC1FTziOkloL+N78tppLM8YYE0LhGDDmAnVFpJaIRAP9gCkhrpMxxhz3wq5LSlWzRORG4Cu8YbVjVHVJiKt1JMKum6yAiks7wNoSrqwtRYwUxfvKGmOMOfbCsUvKGGNMGLKAYYwxJiAWMI4yEbHPOAzZeglPxWm9iBzj63YcA8Vm5YQbETlDRE5U1fC5+0kBiUgpEYkJdT2CQURaikhFWy/hpZitlwoiEqfF8ASxBYyjQES6AOM4wn9RhiMR6QW8A3whIj1E5ORQ16mg3Hp5A+9qAkWarZfw5NbLeOBzEblGRP51lYqizEZJBZmIdAWeBK5V1dnuF+D+ovjLSURq4Q1vvhSoD7QBNgJTVPXnUNbtSInI+cBQ4GpVXSAikapa0MsphJStl/AkIlWAGUB/oCKQBNQAPlTVaaGsW7CE3f8wioGzgZIuWFQCHgXKish3wPequii01TsiZYE0VZ2Ld9XgZXgXgjxPRLaq6l+hrd4R6Q1UdV9KZYEH3fr5GPhJVf8ObfWOiK2X8BQNrFbVBQAikgp0BXq59TI/pLULAuuSCjJVvROYKSJzgcnAz8BHeL80uokTyjoGSlV/AXa4P1KiqvPw/nVfHWgQyrodKVUdAMxyX66fAqvxripwEdAxlHULlIiUgAPrZWtRXi/uKg656+X7Ir5eKgCo6iq89fK0m14JfA1sAJq4vEVi38+PBYwgEJF2ItJLRC4DUNUr8Tb6z1X1JVV9H68L4QwgOpxPholIsogMFJEhLulNoLaI9AVwv2p/BK7P/QILVz5tuR5AVS8EFgEzVfU5VX0e+By4WETC+mhbRM4FHhKR2i7pXaBOEV0v5wJDRaQugKr2puiul67AoyJS0SU9BsSJyJ0AqvoH3ndBPxGJDed9PxAWMApJRLrjXRbgFOA+EXkWQFWvB3zvFFgRyAbCdmd2bXkBiMVry2BgOrAMaCcid7isGUA6ELa/lvzacrfPDtwXr9sjt+4RwE7Cf1/oAPQAzhKRqsCXwFKgdW7bKALrxcltS0cRaQAH1st/fIbVhv16cdvYMGC8qm52yUvxehTqicgol1Ya2I93qaMiLayjd7hzv5AexjvB/YOIvAU8JyKJwMbck3cicgNwJXClqqaHrsb582nLTao6Q0TS8frKq6vqqyJyDnCt20kqA5eqamYIq5yvfNpSWkRaquocVd3v8l0DXIu3XsKyLT5WAJuA1kA54Bm8LpwNwGUiMp0wXy8+ctvSBu/83kZgL7BXVXOKwnoRkerAW8AzqpoiIicCNYE4VZ0mIquB4SIyFa+rcICq7g5djYPDRkkVgvtiaqaqE8W7tWw54DO8ER9L3K+lOOAh4E1VXRy62h6aiFQDyqnqry7gLQGmArWAeap6m8tXF9iqqltCV9tDy6ctn+Pt0EtU9Xo3ouUB4MUwXy+iqioiNfFOoH4P3IJ3FFECuFlVd4lIPWBLmK+X/NqieD9ObgRKAf8HvBDm6yUeGAC0wDtPcRXeXUG7AV+p6g0uXyUgU1V3hKquQaWq9jjCB94J7BJACZ+03OD7DlDLvT7VPUeEus4BtKWkmy4BdAH6uulSwB/AFaGuaxDaUhJIxfsVDhAT6jofoi3V8UbdxLnpk/D6+AGuw+t6GgdUCnVdg9SWsUB8EVgvNVxbYt30DcB24FY3XQr4HRgY6roejUfY9g+GK3fCbirwEvBObh8s/3Tvlcc76XUZ8KH7hRGWh3E+bXkRGCsiDdTrrvle3VGTqu7BO8Ea1rfSDLAtGcB7wG4AVd0Xuhrnz7XlC7xzMG+KSCP1hsp+JiJX4/0qfwivT7xv7oijcHQEbYkCLheREmG+XnK3sXEiUkdVXwR6qOpIn/3lQ8J8fymwUEesovLA6wKoDiwGkoFE4A5gHdDYJ98YYBLwg296OD3yacudri2nuDwR7rk/3tDgOqGu93HeltrA5UAmcIHL3wLvPwwhr/tx2Ja7gL+BRn7b2CXAwnDdxgr9WYS6AkXpgfeLbjTeJQxyu6BuwbuFbH03/Qxet0eDUNe3EG2p56YvAebnfvGG6+M4aMttwCq8kXbxLi1suzmPo7bc6reNnQ/MC/dtrDAP65IKgIjUEZEWeCe14/H6wBVAVZ8DngPudye+vwG6qOqyUNX3UI6gLRF4fbE9VfXXUNX3UI6jtjyL92X1FLDftScsuznhuGrLSA7e9/8Ezg/XbSwoQh2xwv2BN158EfA/vH7Y8/F+Id3nk6cm8Fqo6xrEtowOdV2tLXm25VXcr9twfRynbQn7bSxYD/sfxiGISFu8X0KXqOrPIjIaaAm0BWa7XxUTgPZAMxEpr6pbQ1fj/B1hW5qLSIKqhuWJu+O4Lafj/dK1thxlxWkbC6pQR6xwfuBtHFf4TFfCu9wHwMl4J7hfwusbbxLq+lpbrC3WFmvL0XzYH/cOwf2KiFPVne51Zbx/13ZX1XUichLeSa84DfM/5lhbwpO1JTwVp7YEk530PgRVzVbVnW5S8P6gs9VtMJcB9+P9eS/sNxhrS3iytoSn4tSWYLIjjCMkImPxxpJ3wTtkDdvLFxyOtSU8WVvCU3FqS0FZwAiQiOReu2epe+6sqitCW6uCsbaEJ2tLeCpObSksCxhHSESuAOaq6pJQ16WwrC3hydoSnopTWwrKAsYRyr3iZqjrEQzWlvBkbQlPxaktBWUBwxhjTEBslJQxxpiAWMAwxhgTEAsYxhhjAmIBwxhjTEAsYBhjjAmIBQxjjDEB+X8KMf9ezz2BFQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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6UFdERALbZ599xo4dO4oP0HUT129BqQ9KRMQ3CgsLeeaZZ4iMjHTN0PKSXB9Q6oMSEfGN2bNnk5qayp/+9CdCQtwXB+6rSEREfC4vL49HH32UyMhIRo4c6XQ5pVIflIhINfTGG2+wa9cuvv76a0JDQ50up1TaghIRqWays7N58skniY+PZ9CgQU6Xc04KKBGRambSpEkcOXKEF154wXUj90pyfUBpFJ+ISNXZuHEjr732Gvfddx9du3Z1upzzcn1AaRSfiEjVKDrXXqNGjXjmmWecLqdMGiQhIlJNTJs2jVWrVvHee+/RoEEDp8spk+u3oEREpPLS09N55JFHuO6667jjjjucLqdcFFAiIkHOWsvYsWMJCQnhrbfecvXAiJK0i09EJMi99tprLFmyhDfeeIMWLVo4XU65aQtKRCSIbd26ld///vcMHjyYcePGOV3OBXF9QGmYuYhIxeTm5jJq1Cjq1KnD22+/HTC79oq4PqA0zFxE5MJZa7n33nvZuHEj77zzDk2aNHG6pAvm+oASEZEL9+qrr/Lee+8xadIkhgwZ4nQ5FaKAEhEJMkuWLGHixIkMGzaMxx9/3OlyKkwBJSISRPbs2cOtt95K+/btef/99115nafyCtzKRUTkNFlZWQwdOpSCggK+/PJL6tat63RJlaLjoEREgsDRo0dJSEhg586dzJs3jzZt2jhdUqUpoEREAtzx48dJTExk06ZNfPHFFwwYMMDpkqqE63fx6TgoEZFzy83N5aabbiIpKYkZM2Zw4403Ol1SlXF9QOk4KBGR0uXn5zNy5EgWLlzIO++8wy233OJ0SVXK9QElIiJnKygo4M477+Srr75i6tSpjB492umSqpwCSkQkwBQWFjJu3DhmzpzJn//8Z8aPH+90ST6hQRIiIgEkPz+fF154gfnz5zNp0iQeeeQRp0vyGW1BiYgEiGPHjjFkyBDmz5/PE088waRJk5wuyae0BSUiEgAOHDjA4MGDSUlJ4ZFHHgn6cAIFlIiI66WlpZGQkEBWVhZz584lPDzc6ZL8Qrv4RERc7J///CexsbH8/PPPLF++nISEBKdL8hsFlIiIC1lref7550lISCAiIoKVK1fSvXt3p8vyK+3iExFxmZ9++okxY8bwj3/8g1/96le89dZb1K5d2+my/E4BJSLiItu2beOmm25i586d/OUvf+HBBx8MuEu1VxUFlIiIC1hr+eCDD5gwYQIXX3wxixYtIi4uzumyHOX6PiidLFZEgt1PP/3EqFGjGD16NN27d2fDhg3VPpwgAAJKJ4sVkWC2atUqunbtyieffMLTTz/NkiVLiIiIcLosV3B9QImIBKO8vDyeeuop+vbtS2FhIcuXL+exxx4jNDTU6dJcQ31QIiJ+tmbNGn7zm9+QkpLCbbfdxuuvv079+vWdLst1tAUlIuInx48f53e/+x19+vTh8OHDfPnll8yYMUPhdA7aghIR8YN//vOf3HPPPaSnp3Pffffx/PPPo77189MWlIiID2VmZjJ69GhuuOEGatasyYoVK3j99dcVTuWggBIR8YFTp04xdepU2rZty4wZM/jTn/7Epk2b6Nu3r9OlBQzt4hMRqWIrVqzgt7/9LcnJyQwcOJBXX32VyMhIp8sKONqCEhGpIjt37mTEiBFcc801ZGdnM2vWLBYuXKhwqiAFlIhIJWVmZvLAAw8QGRnJ/PnzefLJJ0lLS2P48OHV9jx6VUG7+EREKujEiRP89a9/5bnnniMnJ4e7776bJ554giZNmjhdWlBQQImIXKD8/Hzeeustnn76aQ4cOMCNN97In//8Z+3Kq2LaxSciUk6FhYV89NFHdOjQgfHjx9O6dWuWL1/O3LlzFU4+oIASESnDqVOn+PDDD+ncuTOjRo2ibt26fP3116xYsYJ+/fo5XV7QUkCJiJxDbm4ub7zxBu3ateOOO+4gJCSEjz/+mA0bNjB48GANgPAx9UGJiJwhJyeHadOmMWXKFA4cOEDPnj15+eWXSUxMJCRE3+v9xScBZYx5B0gEDlprO3mn/T9gELDJWnund9oooJG19mVf1CEiciGysrKYOnUqr7zyCocPH2bAgAF88MEHDBgwQFtLDvDVV4HpQELRHWNMPaC7tTYayDPGdDbGXAzcBUz1UQ0iIuWyY8cOxo8fT/PmzZk0aRJXX301K1euZPHixQwcOFDh5BCfbEFZa5cbY1qVmFQIhBnPWq4F5AMPA3+11ub7ogYRkfOx1rJixQqmTJnCnDlzCAsLY9SoUTz00EN06tTJ6fIEP/VBWWuPGWPmARuBxcBRoJe19ml/LF9EpMjJkyeZOXMmU6dOZf369TRs2JDHHnuMCRMm0LhxY6fLkxKMtdY3L+zZgppb1Ad1xmNvAa8D3YHrgWRr7TOlzDcOGAfQuHHjHjNnzvRJrZWVk5NDnTp1nC7Dp9TG4FCd27hv3z6++uorvvnmG44dO0bLli25+eabuf766wkPD3eg0ooLtvXYv3//9dbamLMesNb65Aa0AraUMr0b8DZQG1jgnfYu0PZ8r9ejRw/rVkuXLnW6BJ9TG4NDdWvjqVOn7Jw5c2xCQoIFbGhoqB0xYoRdunSpLSwsdK7ISgq29Qiss6V87jsxzPxpPFtFYUCod1ohnr4pEZFKS09P59133+Xdd99l7969NG3alEmTJnH33XfTrFkzp8uTcvLVMPOPgTigkTEmA5hkrX3bGDMMT1Lu9863yRiTgmcX3+ZzvNYQYEibNm18UaqIBImff/6ZL774ghdffJH169cDEB8fz5QpUxg2bBhhYWEOVygXylej+G47x/QvgC9K3H8Yz2i+873WHGBOTEzM3VVYoogEieTkZN5++20+/PBDDh8+TOPGjXn88ce56667aNmypdPlSSXoTBIiEnCOHj3KzJkzefvtt1m7di01atRg2LBhjB07ltDQUAYOHOh0iVIFXB9Q2sUnIgB5eXnMnz+fjz76iDlz5nDy5Ek6d+7Myy+/zKhRo2jYsCEAy5Ytc7ZQqTKuDyjt4hOpvgoLC1m+fDkzZsxg1qxZHDlyhEaNGnHXXXcxZswYYmJidJaHIOb6gBKR6sVay8aNG5kxYwYzZ85k37591K5dm5tuuonbb7+dgQMHasBDNaGAEhFX2LVrFx9//DEzZsxg27ZthIWFMWjQIKZMmcKQIUOoVUtHolQ3rg8o9UGJBK9t27Yxe/ZsPv/8czZs2ADAtddey0MPPcSIESO49NJLHa5QnOT6gFIflEjwsNayefPm4lDaunUrAL179+aFF15g5MiRNG/e3OEqxS1cH1AiEtgKCwtZs2ZNcSj961//IiQkhGuuuYb77ruPYcOGERER4XSZ4kIKKBGpcgUFBaxYsYLZs2cze/Zs9u3bR1hYGAMHDuTRRx9l6NCh/OIXv3C6THE5BZSIVInjx4+zaNEi5syZw1dffcWhQ4cIDw8nISGByZMnk5iYSP369Z0uUwKI6wNKgyRE3Gvfvn3MnTuXOXPmsHjxYnJzc7nkkksYPHgww4cPZ9CgQdSuXdvpMiVAuT6gNEhCxD0KCwvZuHEjc+bMYc6cOcUj71q3bs0999zDkCFD6NevHzVq1HC4UgkGrg8oEXFWdnY2CxcuZN68ecyfP58ffviBkJAQ+vTpw+TJkxkyZAgdO3bUGR2kyimgROQ01lqSk5OZN28e33zzDUlJSRQUFNCgQQNuuOEGBg0axODBg2nUqJHTpUqQU0CJCAcPHmTJkiUsXLiQ+fPns3//fgC6devGH/7wBwYPHkzPnj256CJ9ZIj/uP7dpkESIlXvxIkTrFixgkWLFrFw4UI2b/ZcL7R+/frEx8czePBgEhISaNq0qcOVSnXm+oDSIAmRyisoKGDDhg189NFHPPXUU3z//ffk5eVRo0YNYmNjefbZZ4mPj6dHjx6EhoY6Xa4IEAABJSIVs3v37uItpCVLlnDkyBEAunTpwv333891111H3759NQxcXEsBJRIksrKyWLx4MYsWLWLRokXs2bMHgIiICIYNG8Z1111HzZo1ufnmmx2uVKR8FFAiAerQoUMsX76cb7/9lmXLlpGSkgLAJZdcQv/+/Zk4cSLx8fG0a9eueAi4rjYrgUQBJRIgDh48yLffflscSKmpqQDUqlWLq6++mpEjRzJgwACuuuoqjbaToKB3sYhL/fDDD6cFUlpaGgC1a9emb9++3H777cTFxdGjRw+duUGCkusDSsPMpbrYv3//aYG0fft2AOrUqUO/fv0YPXo0cXFxdO/eXZc8l2rBWGudrqFcYmJi7Lp16yr9OnFxcWXOk5iYyMMPP1w8/5gxYxgzZgyZmZmMGDHirPmzs7NPO0vzmfNPnDiRIUOGsH37du65554yl3/m/M899xyxsbEkJSXxxz/+scznnzn/tGnTaN++PXPmzGHKlCllPv/M+WfNmsWWLVtIT09n+vTpZT5/1qxZNGrUiOnTpzN9+vTifo8XX3yRuXPnlvn8kvOvXLmSzz//HIBHH32UlStXnve5DRs2PG3+rKws3nzzTQDGjRvHjh07zvnc7Oxsevbsedr8DRs25Pnnnwdg+PDhZGVlnXf5ffr0OW3+Pn36nPZeKmKtJTc3l6NHjxbfTp48CXj6kPr160daWhq33347jz/+ONnZ2aW+985U1nvvzPfqmdz43iv5XirLme/VQHnvAbRr167c773S1mN533vncqGfe0Wqol/TGLPeWhtz5nTXb0GJBIOCggJycnJOC6S8vDwALrroIurVq0fTpk0ZMmQIU6ZMITQ0lLi4OFq3bq3+JKm2qt0WlC8sW7asXN9QApnaeGGys7NZvXo1SUlJJCUlsXr1ao4dOwZ4hn3369ePvn370q9fP6KioggJCamS5ZZF6zE4BFsbtQUl4iPWWnbu3FkcRklJSWzduhVrLSEhIXTu3JlRo0YRGxtLv379aNGihc78LVIOCiiRC3TixAnWrl1LUlISK1euJCkpqbh/oH79+vTu3ZuRI0cSGxtLz549qVu3rsMViwQmBZTIeRQWFrJjxw5Wr17NqlWrWL16NcnJyRQUFADQvn17hg4dSmxsLLGxsXTo0MFvu+tEgp0CSqSErKwsVq9eXRxIa9asITs7G4C6devSs2dP/ud//ofY2Fh69+5Nw4YNnS1YJIgpoKTaysvLY/PmzcVhtGzZMvbt2wdASEgInTp14tZbb6VXr1707t1bW0cifub6gNKBulIVCgsL2bVrF2vWrCm+bdy4sXiod5MmTWjTpg33338/vXr1IiYmhjp16jhctUj15vqA0vWg5EJZa9m3bx/r1q1j3bp1rFmzhrVr1xbvqqtVqxYxMTE88MAD9OzZk169etG8eXO+/fbboBq6KxLoXB9QImU5cOBAcRitX7+edevW8eOPPwIQGhpavKuuZ8+e9OzZk44dO+rgV5EAoP9SCSiHDh0qDqOi2/79+wFPv1FkZCSDBg2iR48exMTE0KVLFy6++GKHqxaRilBAiSsV7abbuHEjGzZsYOPGjWzcuJF///vfABhjaN++PQMGDCAmJoaYmBi6du2qq8OKBBEFlDiuaADDmWGUmZkJeMKoXbt2xMbG8sADDxATE0O3bt245JJLHK5cRHxJASV+lZeXx9atW08Lo82bN5OTkwNAWFgYnTp1YujQoXTr1o3u3bsTHR2tEXUi1ZACSnzm+PHjbN68+bQwSk1NLR7aXbt2bbp27cqYMWOKwygyMlIX3xMRQAElVSQrK6t411xRIO3YsYOis+U3atSIbt268eCDD9K9e3e6detGmzZtdOCriJyTAkouiLWWjIyMs8Jo7969xfO0aNGCbt26cdtttxWHUbNmzXQGbxG5IAooOafjx4+TmppKSkoK8+bN48knnyQ5OZnDhw8D/xlJ17dv3+Ig6tq1q85PJyJVQgElFBYWsmfPHlJSUkhOTi6+7dq1q3gXXXh4OF27dmXEiBFER0cXD17QsG4R8RXXB5TOxVe1srOzzwqilJQUjh8/Dni2itq0aUN0dDSjRo0iOjqa6Oho0tPTGTBggMPVi0h14vqA0rn4KubUqVPs2LHjtCBKTk4+ra+oQYMGdOnShbFjx9K5c2eio6OJiooqdauo6ABZERF/cX1ASdl+/PHHs7aItm7dys8//wzARRddRIcOHejXr1/xFlF0dDSXX365Bi6IiGspoAJIbm4uW7duPS2IkpOTOXjwYPE8TZs2JTo6mvj4+OIg6tChg44tEpGAo4Byoby8PHbu3Elqauppt507dxZfajw8PJxOnTqRmJhIdHQ0nTt3pnPnzlx22WUOVy8iUjUUUA7Kz88/ZxCdOnUK8Jyh+8orryQqKorhw4fTpUsXoqOjadOmDaGhoQ63QETEdxRQfnDq1Cl27dp1VhDt2LGD/Px8wDN6rnXr1kRFRTFs2DCioqKIioqiffv2ulyEiFRLCqgqVFBQwO7du88Kou3btxeffw7giiuuICoqisTExOIg6tChA7Vq1XKwehERd1FAVUBBQQF79uwpDqAlS5bw4IMPsm3btuKRcwAtW7YkKiqKhISE4iDq2LGjDm4VESkHBdR5FBYWkp6eftYW0bZt2zh58mTxfL/4xS/o3r078fHxpwVR3bp1HaxeRCSwKaD4TxClpaWdFkRpaWmcOHGieL5mzZoRFRVFXFxccRBFRkayYcMG4uLinGuAiEgQqlYBlZ+fz+7du9m6dStpaWnFP8/cImratClRUVHcfffdpwVR/fr1nSteRKSaqTYBtXjxYgYNGlQ8ag48l4WIjIwkLi6OyMhIOnbsSGRkJA0aNHCwUhERgWoUUO3bt2fixInFQdShQwddRlxExMWqTUBFRETw/PPPO12GiIiUk663LSIirqSAEhERV1JAiYiIKymgRETElRRQIiLiSgooERFxJQWUiIi4kgJKRERcyVhrna6hXIwxh4D/c7qOc2gEZDpdhI+pjcFBbQwOwdbGltbay86cGDAB5WbGmHXW2hin6/AltTE4qI3BoTq0EbSLT0REXEoBJSIirqSAqhpvOl2AH6iNwUFtDA7VoY3qgxIREXfSFpSIiLiSAkpERFxJAeUjxhj9bYOA1mNwqA7r0RhjnK6hqgX9SvM3Y8w1xpgm1tpCp2vxFWNMLWNMTafr8CVjTE9jTCOtx8BWTdZjQ2NMbRuEAwoUUFXIGHM98B7Q0ulafMUYczPwIfCNMSbRGNPa6Zqqmnc9vg00c7oWX9F6DA7e9fgx8LUx5m5jTC+na6pKGsVXRYwxNwB/Bu6x1q7yfjPND6ZvbsaYK4AFwO1Ae6APcBD4ylq70cnaqooxZijwBPAba+0GY0yotbbA4bKqlNZjcDDGXA4sBW7Dc+qjGKAF8Lm1dqGTtVWVi5wuIIhcB1zsDafLgOeAS4wxy4EV1tpkZ8urEpcAGdbatcBaY8w24JfAEGPMYWutW8+VeCFGAM28H2qXAJO86/MfwGpr7X5ny6sSWo/BsR5rAP+21m4AMMbsAm4Abvaux/WOVlcFtIuvilhrHwa+N8asBb4ENgKz8XyjSTBeTtZYWdbazcBRY8xvvffXAV8BzYEOTtZWVay1dwJJ3g/tOcC/gbXAcKC/k7VVljEmDIrX4+FgXI/GmBpQvB5XBOl6bAhgrU3Hsx5f9N7/F/BP4Eegs3fegP7MUUBVgjHmamPMzcaYUQDW2rvw/BN8ba193Vr7CZ5dKdcANQKxE9MYE2eMGW2Mudc76V3gSmPMrQDeb+ErgfFFH4CBpkQbxwNYa28CkoHvrbWvWGv/CnwNjDTGBOReB2PMjcCTxpgrvZM+AtoE2Xq8EXjCGNMWwFo7guBbjzcAzxljGnknPQ/UNsY8DGCt3Y3nM+hXxpjwQPzMKUkBVUHGmMF4TjfSCXjUGPMSgLV2PDC5xKyNgAIg4P7pvW18DQjH08ZxwGJgG3C1MWaid9aTQA4QcN/Wzmjj70v8o9+KZ7dQUZtCgJ8I3P+ZfkAiEG+MaQbMB9KA3kVtJoDXo1dRG/sbYzpA8Xr8U4lh5gG7Hr3v1WeAj621RZfaSMOzp6adMeZV77Q6QD4Q6v8qq1ZAfotwmvcb2lN4BkR8Z4x5H3jFGNMYOFjUGWuMmQDcBdxlrc1xruILV6KN91trlxpjcvD0XTS31k4zxgwC7vH+0zQFbrfW5jlY8gU7RxvrGGN6WmvXWGvzvfPdDdyDZz0GVBtL2AkcAnoD9YEpeHZ9/QiMMsYsJkDXYwlFbeyDp//3IJAL5FprCwN5PRpjmgPvA1OstcuMMU2AVkBta+1CY8y/gWeNMfPw7Kq901p73LmKq4ZG8VWA94Otm7X2U2NMKJ5/+Ll4Rgyler+t1QaeBN611qY4V23FGGMigPrW2i3e4E0F5gFXAOustQ9552sLHLbWZjlXbcWco41f4/nHT7XWjveOlHocmBqg69FYa60xphWeDvQVwH/j2UoKAx6w1h4zxrQDsgJ0PZ6rjRbPl6rfArWA/wVeC9D1WA+4E7gKTz/TfwFbgQRggbV2gne+y4A8a+1Rp2qtUtZa3cp5wzPgIQwIKzGtKOQ/BK7w/h7t/RnidM2VaOPF3vthwPXArd77tYDdwBina/VhGy8GduHZmgCo6XTNFWhjczyjvGp777fE0xcDcB+eXXnvAZc5XauP2zgdqBfA67GFt43h3vsTgGzgQe/9WsB2YLTTtfriFnD7YZ3i7YCdB7wOfFi0j5v/7Ca9FE9n5Sjgc+83mYDaPC3RxqnAdGNMB+vZzbXCercWrbUn8HSwH3Gy1ooqZxtPAjOA4wDW2p+dq/jCedv4DZ6+tXeNMZHWM3R8rjHmN3i2Lp7E00dxa9HIt0ByAW28CLjDGBMWoOux6L36njGmjbV2KpBorX25xP/j5wTo/2OZnE5It9/w7AppDqQAcUBjYCJwAIgqMd87wCzgu5LTA+F2jjY+7G1jJ+88Id6ft+EZQt/G6brVxgtq45XAHUAeMMw7/1V4jhVyvHa1scw2PgLsByK98xS9V38NbAq092q5/xZOFxAINzzfNN/Ec8qUol16/w3sA9p770/Bs1uog9P1+qCN7bz3fw2sL/pAD7RbNW7jQ0A6nhGl9bzTAm73s9rIg2e8V4cC6wL1vVqem3bxnYcxpo0x5io8gyDq4emTsADW2leAV4A/egdKLAKut9Zuc6reiriANobg2df9S2vtFqfqrQi10b6E58PuBSDf286A2v0MaqO19mVO/8zZAwwNtPfqBXE6Id16w3M8RTLwLZ793EPxfEN7tMQ8rYC/O12rH9r4ptO1qo1V0sZpeL+NB9pNbTytjQH7Xr3Qm46DKoUxJhbPN7FfW2s3GmPeBHoCscAq77eXmUBfoJsx5lJr7WHnKr5wF9jG7saYBtbagOqIVRvPamMPPN/M1UaXqQ7v1YrQcVCl8L5Z2llrp3vvXwZMt9beaDyXJXgMzwGAvfAMtw7E4yrURrUxIKiNwdHGilBAlcL7baW2tfYn7+9N8Rx1P9hae8AY0xJPZ2VtG6AHxKmNamOgUBuDo40VoUESpbDWFlhrf/LeNXgOjDvsfaOMAv6I52DdgH2jqI1qY6BQG4OjjRWhLahyMsZMx3OsxfUE6Sa22hgc1MbgUB3aWBYFVBmMMUXnLEvz/hxord3pbFVVS20MDmpjcKgObSwvBVQ5GWPGAGuttalO1+IramNwUBuDQ3VoY1kUUOVkjOeMyU7X4UtqY3BQG4NDdWhjWRRQIiLiShrFJyIirqSAEhERV1JAiYiIKymgRETElRRQIn5ijCkwxmwyxqQaYzYbYyZ6Lwtxvue0Msb82l81iriJAkrEf05aa7taa6OA64BBwKQyntMKz0UURaodDTMX8RNjTI61tk6J+62BtXiuAtsS+ACo7X34t9baJGPMKqAjnovTvQe8CkzGcynwmsBUa+00vzVCxI8UUCJ+cmZAeadlA+2BY0ChtTbXGNMW+NhaG2OMiQMettYmeucfB/zCWvuMMaYm8D1wi7V2jx+bIuIXumChiDuEAa8ZY7oCBUC7c8x3PRBtjBnhvV8PaItnC0skqCigRBzi3cVXABzE0xf1I9AFT99w7rmeBtxvrV3glyJFHKRBEiIO8F4x9Q3gNe/51uoBB6y1hcAdQKh31mNA3RJPXQDcZ4wJ875OO2NMbUSCkLagRPznYmPMJjy7807hGRTxF+9jrwOfG2PuBOYDx73Tk4ECY8xmYDrwCp6RfRu8l2U4BAzzT/ki/qVBEiIi4kraxSciIq6kgBIREVdSQImIiCspoERExJUUUCIi4koKKBERcSUFlIiIuNL/B31I9KYPfG0fAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_loan_dynamics(p, r, T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 3B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How much would the Svenssons pay for the same mortgage if their interest rates were 3% or 6%? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameters:\n",
    "- `P = 2_500_000`\n",
    "- `r1 = 0.030`, `r2 = 0.045`, `r3 = 0.060`\n",
    "- `T = 30`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "from src.plotting import plot_rate_difference\n",
    "\n",
    "p, r1, r2, r3, T = 2_500_000, 0.030, 0.045, 0.060, 30\n",
    "plot_rate_difference(p, r1, r2, r3, T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Principal [SEK] | Rate [%/Y]   | Term [Y] | $\\eta$ [%] | $I/A$ [%]   |\n",
    "|-----------------|--------------|----------|------------|-------------|\n",
    "| 2 500 000       | 3.0          | 30       |  51.78     |  51.78      |\n",
    "| 2 500 000       | 4.5          | 30       |  82.41     |  82.41      |\n",
    "| 2 500 000       | 6.0          | 30       | 115.84     | 115.84      |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe that the equality $ \\eta = \\frac{I}{A} $ implies that **the net profit for the lender is the payed interest.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 3C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How much would the Svenssons pay if they decide to pay off the loan, with the original parameters, in 10 or 20 years instead? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameters:\n",
    "- `P = 2_500_000`\n",
    "- `r = 0.045`\n",
    "- `T1 = 10`, `T2 = 20`, `T3 = 30`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "from src.plotting import plot_term_difference\n",
    "\n",
    "p, r, T1, T2, T3 = 2_500_000, 0.045, 10, 20, 30\n",
    "plot_term_difference(p, r, T1, T2, T3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Principal [SEK] | Rate [%/Y]          | Term [Y] | $\\eta$ [%] | $I/A$ [%] |\n",
    "|-----------------|---------------------|----------|------------|-----------|\n",
    "| 2 500 000       | 4.5                 | 10       | 24.37      | 24.37     |\n",
    "| 2 500 000       | 4.5                 | 20       | 51.84      | 51.84     |\n",
    "| 2 500 000       | 4.5                 | 30       | 82.41      | 82.41     |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time Value of Money"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 3D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider the same scenario in which the Svenssons what to borrow 2 500 000 SEK with interest rate 4.5% and they can choose either loan term 10, 20 or 30 years. Assume that money markets offer a flat continuously-compounded rate of 1.5% over the same period. How does this affect the valuation of future cash flows?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameters:\n",
    "- `P = 2_500_000`\n",
    "- `r = 0.045`\n",
    "- `T1 = 10`, `T2 = 20`, `T3 = 30`\n",
    "- `rf = 0.015`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "from src.plotting import plot_term_difference\n",
    "\n",
    "p, r, T1, T2, T3, rf = 2_500_000, 0.045, 10, 20, 30, 0.015\n",
    "plot_term_difference(p, r, T1, T2, T3, 0.015)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Principal [SEK] | Rate [%/Y]          | Term [Y] | $\\eta$ [%] | $I/A$ [%] |\n",
    "|-----------------|---------------------|----------|------------|-----------|\n",
    "| 2 500 000       | 4.5                 | 10       | 15.41      | 25.06     |\n",
    "| 2 500 000       | 4.5                 | 20       | 31.09      | 55.26     |\n",
    "| 2 500 000       | 4.5                 | 30       | 46.80      | 91.69     |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sensitivities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Net profit $\\eta$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Net profit is defined as the sum of all payments divided by the initial principal\n",
    "\n",
    "$$ \\eta = \\frac{A \\, T}{P}, \\qquad (2)$$\n",
    "\n",
    "and represents the return on the loaned capital for the lender and the total loan cost for the borrower. Substituting (1) in (2) gives\n",
    "\n",
    "$$ \\eta = \\frac{r \\; T}{1 - \\left( \\frac{1}{1 + r} \\right)^T}. \\qquad (3)$$\n",
    "\n",
    "The total change of the net profit with respect to $r$ and $T$ is approximated with Taylor expansion\n",
    "\n",
    "$$ \\mathrm{d} \\eta \\approx \\frac{\\partial \\eta}{\\partial r} \\mathrm{d}r + \\frac{\\partial \\eta}{\\partial T} \\mathrm{d}T + \\frac{1}{2!} \\frac{\\partial^2 \\eta}{\\partial r^2} {\\mathrm{d}r}^2 + \\frac{\\partial^2 \\eta}{\\partial r \\partial T} {\\mathrm{d}r}{\\mathrm{d}T} + \\frac{1}{2!} \\frac{\\partial^2 \\eta}{\\partial T^2} {\\mathrm{d}T}^2, \\qquad (4)$$\n",
    "\n",
    "where $\\frac{\\partial \\eta}{\\partial r}$, $\\frac{\\partial \\eta}{\\partial T}$, $\\frac{\\partial^2 \\eta}{\\partial r^2}$, $\\frac{\\partial^2 \\eta}{\\partial r \\partial T}$ and $\\frac{\\partial^2 \\eta}{\\partial T^2}$ are the sensitivities and $\\mathrm{d}r$ and $\\mathrm{d}T$ are the respective changes of $r$ and $T$. These derivatives are very similar to the so-called greeks in the option pricing theory."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first-order terms are dominant for small changes in $r$ and $T$. These can be expanded\n",
    "\n",
    "$$\\frac{\\mathrm{d}\\eta}{\\mathrm{d}T} = r \\frac{1 - \\left( \\frac{1}{1 + r}\\right)^T \\left(1 - T \\ln \\left( \\frac{1}{1 + r} \\right)\\right)}{\\left( 1 - \\left( \\frac{1}{1 + r} \\right)^T \\right)^2},$$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \\frac{\\mathrm{d}\\eta}{\\mathrm{d}r} =  T \\frac{1 - \\left(\\frac{1}{1 + r}\\right)^T \\left( 1 + r T \\left(\\frac{1}{1 + r}\\right)\\right)}{\\left(1 - \\left(\\frac{1}{1 + r}\\right)^T\\right)^2}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interested reader is encouraged to find the higher-order derivatives and apply (4) on the problem setup given in **Example 3**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 4A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the net profit $\\eta$ for the loan term $T \\in [5,30]$ years when the interest rates are 3%, 4.5% and 6%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameters:\n",
    "\n",
    "- `r1 = 0.030`, `r2 = 0.045`, `r3 = 0.060`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from src.plotting import plot_total_payment_wrt_time\n",
    "\n",
    "r1, r2, r3 = 0.030, 0.045, 0.060\n",
    "plot_total_payment_wrt_time([r1, r2, r3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dashed lines (--) are tangents on the curves at the first point ($T = 5$ years). Because tangents are linear functions it is visually obvious that the net profit is a non-linear and strictly increasing function with respect to $T$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**This is one of the things to keep in mind when planning personal finances.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example 4B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider that the money markets offer a flat continuously-compounded rate of 2% over the same period as the loan. Calculate how much the time value of money affects the valuation of the net profit? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Parameters:\n",
    "\n",
    "- `r1 = 0.030`, `r2 = 0.045`, `r3 = 0.060`\n",
    "- `rf = 0.020`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from src.plotting import plot_total_payment_wrt_time\n",
    "\n",
    "r1, r2, r3, rf = 0.030, 0.045, 0.060, 0.02\n",
    "plot_total_payment_wrt_time([r1, r2, r3], rf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the lenders perspective, with a positive discount rate the value of an investment decreases. Same holds for the borrower their total loan cost decreases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loan term $T$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similar to the sensitivities found for the [net profit](http://localhost:8888/notebooks/Amortized%20Loans.ipynb#Neto-return), it is also possible to solve (1) for the loan term and find that\n",
    "\n",
    "$$ T = \\frac{\\ln\\left(1 - r \\rho^{-1} \\right)}{\\ln\\left( \\frac{1}{1+r} \\right)}, $$\n",
    "\n",
    "where $\\rho = \\frac{A}{P}$ is the percentage of the loan principle that is re-payed each month."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After carrying out a similar analysis to [net profit](http://localhost:8888/notebooks/Amortized%20Loans.ipynb#Neto-return) it is found that the first-order terms $\\frac{\\partial T}{\\partial r}$ and $\\frac{\\partial T}{\\partial \\rho}$ are a good approximation for the small changes of $r$ and $\\rho$. The respective sensitivities are given as\n",
    "\n",
    "$$ \\frac{\\partial T}{\\partial r} = \\frac{1}{(r-\\rho)\\ln\\left(\\frac{1}{1+r}\\right)} + \\frac{\\ln\\left(1 - r \\rho^{-1}\\right)}{(1+r)\\ln^2\\left(\\frac{1}{1+r}\\right)}, $$\n",
    "\n",
    "and\n",
    "\n",
    "$$ \\frac{\\partial T}{\\partial \\rho} =  - \\frac{r}{\\rho (r-\\rho) \\ln\\left(\\frac{1}{1+r}\\right)}. $$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "from src.plotting import plot_term_sensitivity\n",
    "\n",
    "plot_term_sensitivity()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The figures show that $\\frac{\\partial T}{\\partial r} > 0$ and $\\frac{\\partial T}{\\partial \\rho} < 0$ . This means that increasing $r$ increases $T$ while increasing $A$ and repaying the loan faster increases $\\rho$ but decreases $T$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What can we do with this information?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "=> *Inflation helps the borrower but hurts the lender. <=*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1) Before Taking a Loan"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the four parameters that describe an annuity loan\n",
    "\n",
    "- payment $A$\n",
    "- loan principal $P$\n",
    "- interest rate $r$\n",
    "- loan term $T$,\n",
    "\n",
    "we have _direct control_ over\n",
    "\n",
    "- $P$ \n",
    "- $A$ or $T$ because $A = A(r, T)$ and $T = T(r, A)$.\n",
    "\n",
    "and we have _limited control_ over $r$ because $r = r(T)$.\n",
    "\n",
    "=> *We can have good control of all the risks of borrowing money with annuity loan before taking the loan. <=*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2) After Taking a Loan"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Considering the loan with parameters $A$, $P$, $r$ and $T$ we can actively change one of them and the others are indirectly changed.\n",
    "\n",
    "=> *Finding the sensitivities helps in calculating how the total loan cost changes with respect to the changing parameter.* <="
   ]
  }
 ],
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