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:

    “What he loved so much in the plant morphological structure of the tree was that given a fixed mathematical basis, the final evolution was so incalculable.”
    —D.H. (David Herbert)

    “Is whispering nothing?
    Is leaning cheek to cheek? Is meeting noses?
    Kissing with inside lip? Stopping the career
    Of laughter with a sigh?—a note infallible
    Of breaking honesty.”
    —William Shakespeare (1564–1616)