Interest Rate - Mathematical Note

Mathematical Note

Because interest and inflation are generally given as percentage increases, the formulae above are (linear) approximations.

For instance,

is only approximate. In reality, the relationship is

so

The two approximations, eliminating higher order terms, are:

\begin{align} (1+x)(1+y) &= 1+x+y+xy &&\approx 1+x+y\\ \frac{1}{1+x} &= 1-x+x^2-x^3+\cdots &&\approx 1-x \end{align}

The formulae in this article are exact if logarithms of indices are used in place of rates.

Read more about this topic:  Interest Rate

Famous quotes containing the words mathematical and/or note:

    “The circumstances of human society are too complicated to be submitted to the rigour of mathematical calculation.”
    —Marquis De Custine (1790–1857)

    “No, in your rural letter box
    I leave this note without a stamp
    To tell you it was just a tramp
    Who used your pasture for a camp.”
    —Robert Frost (1874–1963)