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:

    “All science requires mathematics. The knowledge of mathematical things is almost innate in us.... This is the easiest of sciences, a fact which is obvious in that no one’s brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.”
    —Roger Bacon (c. 1214–c. 1294)

    “My note to you I certainly did not expect to see in print; yet I have not been much shocked by the newspaper comments upon it. Those comments constitute a fair specimen of what has occurred to me through life. I have endured a great deal of ridicule without much malice; and have received a great deal of kindness, not quite free from ridicule. I am used to it.”
    —Abraham Lincoln (1809–1865)