.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/time_value/annuities/plot_03_price_sinking_fund.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_time_value_annuities_plot_03_price_sinking_fund.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_time_value_annuities_plot_03_price_sinking_fund.py:


Price's sinking fund
====================

In *An Appeal to the Public on the Subject of the National Debt* (1772)
Richard Price showed what compound interest could do for a nation in
debt: a fixed sum set aside every year and left to accumulate at
interest would grow to repay the debt. The level deposit that reaches a
target :math:`F` in :math:`n` periods is :math:`F / s_{\overline{n}|}`.
Pitt's sinking fund of 1786 put the idea into practice.

.. GENERATED FROM PYTHON SOURCE LINES 14-19

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from financialkit.time_value import sinking_fund_payment, sinking_fund_schedule








.. GENERATED FROM PYTHON SOURCE LINES 20-22

Repaying a debt of 1,000,000 in 30 years at 5%
----------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 22-27

.. code-block:: Python


    s = sinking_fund_schedule(1_000_000.0, 0.05, 30)
    print(f"annual deposit: {s.deposit:,.0f}")
    print(f"total deposited: {30 * s.deposit:,.0f}; interest earned: {s.interest.sum():,.0f}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    annual deposit: 15,051
    total deposited: 451,543; interest earned: 548,457




.. GENERATED FROM PYTHON SOURCE LINES 28-30

How interest does the work
--------------------------

.. GENERATED FROM PYTHON SOURCE LINES 30-49

.. code-block:: Python


    fig, axes = plt.subplots(1, 2, figsize=(11, 4))
    deposits = np.full(30, s.deposit)
    axes[0].bar(s.periods, deposits, label="deposit")
    axes[0].bar(s.periods, s.interest, bottom=deposits, label="interest earned")
    axes[0].plot(s.periods, s.balance / 10, "k", label="fund balance / 10")
    axes[0].set_xlabel("year")
    axes[0].legend()

    n = np.arange(5, 61)
    for r in (0.03, 0.05, 0.07):
        axes[1].plot(n, sinking_fund_payment(1_000_000.0, r, n) * n / 1e6, label=f"{r:.0%}")
    axes[1].set_xlabel("years to repay")
    axes[1].set_ylabel("total deposits per unit of debt")
    axes[1].set_title("Longer horizons let interest pay more of the debt")
    axes[1].legend()
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/time_value/annuities/images/sphx_glr_plot_03_price_sinking_fund_001.png
   :alt: Longer horizons let interest pay more of the debt
   :srcset: /api/gallery/time_value/annuities/images/sphx_glr_plot_03_price_sinking_fund_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.074 seconds)


.. _sphx_glr_download_api_gallery_time_value_annuities_plot_03_price_sinking_fund.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/time_value/annuities/plot_03_price_sinking_fund.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_03_price_sinking_fund.ipynb <plot_03_price_sinking_fund.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_03_price_sinking_fund.py <plot_03_price_sinking_fund.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_03_price_sinking_fund.zip <plot_03_price_sinking_fund.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_