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Money and Time

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Illustrating Finance Policy with Mathematica

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Abstract

Discounting moves value through time. This chapter discusses periodic and continuous compounding, annuities, growing annuities, and the internal rate of return.

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Notes

  1. 1.

    In Mathematica:

    \(\boldsymbol{{\tt{limit}}{[\tt{p}}{\tt{(1+}}\frac{\tt{{r}}}{\tt{{n}}}{\tt{)}}^{{\tt{tn}}},{{\tt{ }}}{\tt{n}}\to {\tt{Infinity}]}}\)

  2. 2.

    The Mathematica command is:

    \(\boldsymbol{{\tt{Sum}}\;\tt{[}\frac{{{\tt{a(1+g)}}^{{\tt{i}}} }}{{\tt{(1+r)}}^{{{\tt{i+1}}}} }{\tt{,}} \left\{ {{\tt{i,0,Infinity}}} \right\}\tt{]}}\)

  3. 3.

    The command for obtaining only the real solution from Mathematica is FindRoot[ eqn , { variable , initialguess }] which, using a guess of 7%, becomes in the instance of annual compounding

    \(\boldsymbol {{\tt{FindRoot[ - 100 + }}\frac{{{\tt{10}}}}{{{\tt{1 + r}}}}{\tt{ + }}\frac{{{\tt{10}}}}{{{\tt{(1 + r)}}^{{\tt{2}}} }}{\tt{ + }}\frac{{{\tt{110}}}}{{{\tt{(1 + r)}}^{{\tt{3}}} }}{\tt{ = = 0,\{ r,}}{\tt{\,.07\} ]}}}\)

    which may solve the present question but is somewhat clumsy.

  4. 4.

    See, e.g., Weinberger v. UOP, Inc., 457 A.2d 701 (Del. 1983) (where the Delaware Supreme Court accepts discounting and flexible methods of valuation based on modern finance rather than insisting on the “Delaware block” method of its precedent).

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  1. Indiana University, Indianapolis, IN, USA

    Nicholas L. Georgakopoulos

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  1. Nicholas L. Georgakopoulos
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Correspondence to Nicholas L. Georgakopoulos .

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Georgakopoulos, N.L. (2018). Money and Time. In: Illustrating Finance Policy with Mathematica. Quantitative Perspectives on Behavioral Economics and Finance. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-95372-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-95372-4_4

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  • Publisher Name: Palgrave Macmillan, Cham

  • Print ISBN: 978-3-319-95371-7

  • Online ISBN: 978-3-319-95372-4

  • eBook Packages: Economics and FinanceEconomics and Finance (R0)

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