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:

    “As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.”
    —Blaise Pascal (1623–1662)

    “What says the Clock in the Great Clock Tower?
    And all alone comes riding there
    The King that could make his people stare,
    Because he had feathers instead of hair.
    A slow low note and an iron bell.”
    —William Butler Yeats (1865–1939)