Computing Your Tax

A nice application of Interpolation is to compute how much tax you have to pay. For example, in Australia the income tax thresholds are as follows.

Express these thresholds as a matrix (assuming a maximum salary of $1,000,000).

Then use zeroth-order interpolation to construct the tax rate function, .

A plot of the tax rate shows that it has the required stepwise behavior.

Integrating the tax rate gives the tax as a function of income. Note that indefinite integration using Integrate automatically returns an InterpolatingFunction over the same domain.

Here is a plot of the after-tax income versus gross income.