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)

    “In our Mechanics’ Fair, there must be not only bridges, ploughs, carpenter’s planes, and baking troughs, but also some few finer instruments,—rain-gauges, thermometers, and telescopes; and in society, besides farmers, sailors, and weavers, there must be a few persons of purer fire kept specially as gauges and meters of character; persons of a fine, detecting instinct, who note the smallest accumulations of wit and feeling in the bystander.”
    —Ralph Waldo Emerson (1803–1882)