compound_and_continuous_interest.ipynb

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  "metadata": {
    "colab": {
      "provenance": [],
      "toc_visible": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Compound and continuous interest"
      ],
      "metadata": {
        "id": "4jwoPkO1N1nY"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "Compound interest is given by the following formula\n",
        "\n",
        "\\begin{equation}\n",
        "A=P(1+\\frac{r}{n})^{nt}\n",
        "\\end{equation}\n",
        "\n",
        "Continuous interest is given by\n",
        "\n",
        "\\begin{equation}\n",
        "A=P𝒆^{rt}\n",
        "\\end{equation}\n",
        "\n",
        "Let us calculate a few interests to set this in Python."
      ],
      "metadata": {
        "id": "zgmU5GuHs7E7"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Find the accumulated value of an investment of $ 15000\n",
        "for 7 years at an interest rate of 4.5 % if the money is a. compounded​ semiannually; b. compounded​ quarterly; c. compounded​ monthly; d. compounded continuously."
      ],
      "metadata": {
        "id": "YrI1LQTUQKuw"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Find the accumulated value of an investment of $ 15000 for 7 years at an interest rate of 4.5 % if the money is"
      ],
      "metadata": {
        "id": "X6iox8leTH0p"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "VNIMlzNuiuxB"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import math\n",
        "#A is the Accumulated value\n",
        "P = 15000  #Principal value\n",
        "t = 7 #time in years\n",
        "r = 0.045 #anual percentage rate"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### a. compounded​ semiannually"
      ],
      "metadata": {
        "id": "hpbIMURRTXII"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "n = 2\n",
        "A = P * (( 1 + r / n) **( n * t))\n",
        "print('a.')\n",
        "print(A)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wPllTjl-TqKZ",
        "outputId": "23fcc6e7-a984-4d46-cb8a-55f954d6aec2"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "a.\n",
            "20482.251408598328\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### b. compounded​ quarterly"
      ],
      "metadata": {
        "id": "2hatAOJ1TvJ4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "n = 4\n",
        "A = P * (( 1 + r / n) **( n * t))\n",
        "print('b.')\n",
        "print(A)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "svox_hE5UI2_",
        "outputId": "a176a48c-0af9-4858-8da3-e53a655f8caa"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "b.\n",
            "20517.773367066435\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### c. compounded​ monthly"
      ],
      "metadata": {
        "id": "K8zg7V67T3Oo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "n = 12\n",
        "A = P * (( 1 + r / n) **( n * t))\n",
        "print('c.')\n",
        "print(A)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "35DlWtwIULfX",
        "outputId": "4f284974-13f7-46bd-cac8-8f580d1d8850"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "c.\n",
            "20541.783853707868\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###d. compounded continuously"
      ],
      "metadata": {
        "id": "qSna1Q5cT-9_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = P * (math.e **( r * t))\n",
        "print('d.')\n",
        "print(A)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5RUYJAn2UN5P",
        "outputId": "b9d1293e-8990-4fc9-d56f-9766f9f6c384"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "d.\n",
            "20553.88966435495\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "##Suppose you have $ 11000 to invest. Which of the two rates would yield the larger amount in 3 years​?"
      ],
      "metadata": {
        "id": "-abw5qSGv2lC"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "P = 11000  #Principal value\n",
        "t = 3 #time in years"
      ],
      "metadata": {
        "id": "YbillrHFwMtY"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###6​% compounded monthly"
      ],
      "metadata": {
        "id": "eb-e-pOyVJki"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "r = 0.06 #anual percentage rate\n",
        "n = 12\n",
        "A = P * (( 1 + r / n) **( n * t))\n",
        "print('a.')\n",
        "print(A)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4-6zp5jrVT_Q",
        "outputId": "30960b39-e735-4788-c958-839fc20c91c0"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "a.\n",
            "13163.485773057562\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###5.88 % compounded​ continuously"
      ],
      "metadata": {
        "id": "7vVO1xZ8VU5Q"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "r = 0.0588\n",
        "A = P * (math.e **( r * t))\n",
        "print('b.')\n",
        "print(A)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cj7JTmiUVZxA",
        "outputId": "c8d7a82f-2938-4ed0-9d54-f4729d6c9add"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "b.\n",
            "13122.066422100846\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "In this case, it's clear that the monthly interest yields more."
      ],
      "metadata": {
        "id": "__R46Mki4mtQ"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##You have ​$14000 to invest. One bank pays 0.6​% interest compounded semiannually and a second bank pays 0.45​% interest compounded monthly. "
      ],
      "metadata": {
        "id": "lj7G41okXdTq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can write a function for the balance in each bank at any time t.\n",
        "\n",
        "For the balance in the first bank with interest compounded semiannually at any time t.\n",
        "\n",
        "\\begin{equation}\n",
        "A=14000(1.003)^{2t}\n",
        "\\end{equation}\n",
        "\n",
        "For the balance in the second bank with interest compounded monthly at any time t.\n",
        "\n",
        "\\begin{equation}\n",
        "A=14000(1.000375)^{12t}\n",
        "\\end{equation}"
      ],
      "metadata": {
        "id": "ihdsMGX0wY1A"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "###Which bank offers the better return on your​ money?"
      ],
      "metadata": {
        "id": "rOdB90pT7qZU"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "t = np.linspace(0, 50, 100)\n",
        "A = 14000*((1.003)**(2*t))\n",
        "\n",
        "\n",
        "fig = plt.figure(figsize = (10, 5))\n",
        "a = plt.plot(t, A,'r')\n",
        "A = 14000*((1.000375)**(12*t))\n",
        "b = plt.plot(t,A)\n",
        "plt.legend((a[0], b[0]), ('1st bank semianually', '2nd bank monthly'), bbox_to_anchor=(0.04, 0.82, 0.9, 0.102))\n",
        "\n",
        "plt.show()"
      ],
      "metadata": {
        "id": "7jSwQ3Rlwjyh",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 445
        },
        "outputId": "f0140452-98f7-4859-d05f-f5c20d17f3ef"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The first bank does, as seen in the graph."
      ],
      "metadata": {
        "id": "yT6YjtvlYFAv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##Complete the table for a savings account subject to n compounding periods per year."
      ],
      "metadata": {
        "id": "0Eg9hFrvjNqI"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "###a.\n",
        "| Amount invested | Number of Compounding Periods | Annual Interest Rate | Accumulated amount |Time t in years |\n",
        "| :-: | :-: | :-: | :-: |:-: |\n",
        "| 15000 | 4 | 6.25% | 22000| |\n"
      ],
      "metadata": {
        "id": "BONu7rrcYZ-g"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = 22000\n",
        "P = 15000\n",
        "n = 4\n",
        "r = 0.0625\n",
        "\n",
        "print(( 1.0 + r / n ))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "egh7XHVojr2h",
        "outputId": "b4067bad-1362-4135-ff5f-c7f2e00624cc"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.015625\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\\begin{equation}\n",
        "\\frac{22000}{15000} = 1.015625 ^ {4t} \\to t=\\frac{Log(\\frac{22500}{15000})}{4Log(1.015625)}\n",
        "\\end{equation}\n",
        "\n"
      ],
      "metadata": {
        "id": "S4YoTw4tn0wJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "t = np.log(A/P) / (n * np.log (1.0+r/n))\n",
        "print('takes '+str(t)+' years to achieve the accumulated value')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dIMHrLbWn0b4",
        "outputId": "9ccd16fc-df56-46b3-d271-b4a468021e63"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "takes 6.175626360139467 years to achieve the accumulated value\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "| Amount invested | Number of Compounding Periods | Annual Interest Rate | Accumulated amount |Time t in years |\n",
        "| :-: | :-: | :-: | :-: |:-: |\n",
        "| 15000 | 4 | 6.25% | 22000| 6.2|"
      ],
      "metadata": {
        "id": "ywBqBEzlqZLu"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "###b.\n",
        "| Amount invested | Number of Compounding Periods | Annual Interest Rate | Accumulated amount |Time t in years |\n",
        "| :-: | :-: | :-: | :-: |:-: |\n",
        "| 50000 | 365 | 11.6% | 137500| |"
      ],
      "metadata": {
        "id": "248ed5E1qs9A"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = 137500\n",
        "P = 50000\n",
        "n = 365\n",
        "r = 0.116\n",
        "\n",
        "t = np.log(A/P) / (n * np.log( 1.0 + r / n ))\n",
        "print('takes '+str(t)+' years to achieve the accumulated value')"
      ],
      "metadata": {
        "id": "tQfiMPmuqtw_",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "96470567-876b-4b6b-cb51-b211d2480a5e"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "takes 8.722083195752266 years to achieve the accumulated value\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "| Amount invested | Number of Compounding Periods | Annual Interest Rate | Accumulated amount |Time t in years |\n",
        "| :-: | :-: | :-: | :-: |:-: |\n",
        "| 50000 | 365 | 11.6% | 137500|8.7 |"
      ],
      "metadata": {
        "id": "mJYRctSma2ch"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "###c. continuous compound\n",
        "\n",
        "The formula \n",
        "\\begin{equation}\n",
        "A = P𝒆^{rt}\n",
        "\\end{equation}\n",
        "\n",
        "describes the accumulated​ value, A, of a sum of​ money, P, the​ principal, after t years at annual percentage rate r​ (in decimal​ form) compounded continuously. "
      ],
      "metadata": {
        "id": "zQyjOKw-qvEg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Complete the table for a savings account subject to continuous compounding.\n",
        "\n",
        "| Amount invested |  Annual Interest Rate | Accumulated amount |Time t in years |\n",
        "| :-: | :-: | :-: | :-: |\n",
        "| 7500 | 9% | 2X| |"
      ],
      "metadata": {
        "id": "4g_YZwJrb4MQ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A = 15000\n",
        "P = 7500\n",
        "r = 0.09\n",
        "\n",
        "t = np.log(A/P)/(r*np.log(math.e))\n",
        "print(t)"
      ],
      "metadata": {
        "id": "p1k4o4beq2DQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6274b0c1-1d0f-4578-c5d5-3b37fa8af3e7"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "7.701635339554948\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "| Amount invested |  Annual Interest Rate | Accumulated amount |Time t in years |\n",
        "| :-: | :-: | :-: | :-: |\n",
        "| 7500 | 9% | 2X|7.7 |"
      ],
      "metadata": {
        "id": "mvSgax_kbZih"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Modeling Inflation"
      ],
      "metadata": {
        "id": "G5n1mVbsce5J"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "The formula \n",
        "\n",
        "\\begin{equation}\n",
        "S = C ( 1 + r ) ^ t\n",
        "\\end{equation}\n",
        "\n",
        "models​ inflation, where C equals the \n",
        "value​ today, r equals the annual inflation rate​ (in decimal​ form), and S equals the inflated value t years from now."
      ],
      "metadata": {
        "id": "jB1luuYVwNsv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "##If the inflation rate is 4 ​%, how much will a house now worth ​$128000 be worth in 9 ​years?."
      ],
      "metadata": {
        "id": "E2Uak4jQdLRR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#S inflated value\n",
        "C = 128000 # initial value\n",
        "r = 0.04 #inflation rate in decimal form\n",
        "t = 9 #time in years\n",
        "\n",
        "S = C * ( 1 + r ) ** t\n",
        "\n",
        "print('The house will be worth: ')\n",
        "print(S)"
      ],
      "metadata": {
        "id": "ujyONn2_wW4Y",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ff5f9b8c-9d4f-402c-e7b7-070d16c77351"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The house will be worth: \n",
            "182183.91198995008\n"
          ]
        }
      ]
    }
  ]
}