Daily Compounding Interest and Float Error Comparisor

compounding_interest.ipynb

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   "source": [
    "# Compounding Interest / Float Innacuracy"
   ]
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    "# this is the way the assignment is expected to be written\n",
    "# (and what the homework grader is expecting)\n",
    "def daily_compounding1(years: int, rate: float, contrib: int) -> float:\n",
    "    balance: float = 0.0\n",
    "\n",
    "    for y in range(years):\n",
    "        for month in range(12):\n",
    "            balance += contrib\n",
    "            for day in range(30):\n",
    "                balance = balance * (1 + rate)\n",
    "    \n",
    "    return balance"
   ]
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   "source": [
    "# this is the way you and I wrote it (difference in last line)\n",
    "def daily_compounding2(years: int, rate: float, contrib: int) -> float:\n",
    "    balance: float = 0.0\n",
    "\n",
    "    for y in range(years):\n",
    "        for month in range(12):\n",
    "            balance += contrib\n",
    "            for day in range(30):\n",
    "                balance += balance * rate\n",
    "    \n",
    "    return balance"
   ]
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   "source": [
    "from decimal import *\n",
    "\n",
    "# this uses the Decimal library to get accurate results, not using floats\n",
    "def daily_compounding3(years: int, rate: float, contrib: int) -> Decimal:\n",
    "    rate = Decimal(rate)\n",
    "    balance =  Decimal(0.0)\n",
    "    \n",
    "\n",
    "    for y in range(years):\n",
    "        for month in range(12):\n",
    "            balance += contrib\n",
    "            for day in range(30):\n",
    "                balance += balance * rate\n",
    "    \n",
    "    return balance"
   ]
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   "outputs": [
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     "execution_count": 23,
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   "source": [
    "years = 5\n",
    "rate = 0.02\n",
    "contrib = 75\n",
    "\n",
    "answer1 = daily_compounding1(years, rate, contrib)\n",
    "answer2 = daily_compounding2(years, rate, contrib)\n",
    "correct = daily_compounding3(years, rate, contrib)\n",
    "\n",
    "# This is the correct answer with no floating-point error\n",
    "\"{:0.2f}\".format(correct)"
   ]
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   "execution_count": 24,
   "id": "4b47b3ff-b5bd-4b15-807c-1acf7de6e32e",
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     "execution_count": 24,
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   "source": [
    "# This is the answer the homework grader is looking for\n",
    "\"{:0.2f}\".format(answer1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "e51cd250-dceb-4138-a642-dc0f83b6a6c0",
   "metadata": {
    "tags": []
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     "data": {
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       "'506012384946505728.00'"
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     "execution_count": 25,
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   "source": [
    "# This is what you originally came up with\n",
    "\"{:0.2f}\".format(answer2)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 29,
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   "metadata": {
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     "data": {
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       "'-16955.59'"
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     "execution_count": 29,
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   "source": [
    "# This is how far off the homework grader's answer is, which is a fair bit\n",
    "# because multiplying the balance by 1.02 compounds floating point error\n",
    "# more than multiplying smaller numbers\n",
    "\"{:0.2f}\".format(correct - Decimal(answer1))"
   ]
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       "'4.41'"
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     "execution_count": 31,
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   "source": [
    "# This is how far off your original answer was, which is a lot closer because\n",
    "# doing multiplication of a small number and then adding that to the balance\n",
    "# keeps the error under control better\n",
    "\"{:0.2f}\".format(correct - Decimal(answer2))"
   ]
  }
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