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)

    “For do but note a wild and wanton herd
    Or race of youthful and unhandled colts
    Fetching mad bounds, bellowing and neighing loud,
    Which is the hot condition of their blood;
    If they but hear perchance a trumpet sound,
    Or any air of music touch their ears,
    You shall perceive them make a mutual stand,
    Their savage eyes turned to a modest gaze
    By the sweet power of music.”
    —William Shake{peare (1564–1616)