# Using clp(QR) This example is extracted from the [OFAI clp(Q,R) Manual](http://www.ofai.at/cgi-bin/get-tr?download=1&paper=oefai-tr-95-09.pdf) by Christian Holzbaur. It defines the _mortgage_ relation between the following arguments: - `P` is the balance at _T0_ - `T` is the number of interest periods (e.g., years) - `I` is the interest ratio where e.g., `0.1` means 10% - `B` is the balance at the end of the period - `MP` is the withdrawal amount for each interest period. @see [Programming with Constraints: An Introduction - Kim Marriott, Peter J. Stuckey](https://books.google.nl/books?id=jBYAleHTldsC&lpg=PA184&ots=QifwRiYDxL&dq=mortgage%20relation%20prolog&pg=PA177#v=onepage&q=mortgage%20relation%20prolog&f=false) which descibes the same example with more background.

We can use the above program to compute the balance if we get an interest of 5% over a period of 30 years.

We can however also compute the linear relation between the initial balance, the final balance and the withdrawal:

In the above we used the _imprecise_ library `clpr`. In the queries we used a rational number for the interest. You can replace `clpr` with `clpq` to get exact results.