Interval Methods in Knowledge Representation (abstracts of recent papers)

that if we place money in the bank that pays this interest and withdraw the amount A every year, we will get exactly 0 after n-th withdrawal. Knowing q enables us to make decisions about whether to invest in this annuity or not: e.g., if this q is smaller than the actual bank's interest rate 90, then it is better to leave the money in the bank; if q is larger than qo, then it is better to invest in an annuity. For a simple annuity, the effective rate of return is a solution to a polynomial equation. There are many known methods of numerical solution of polynomial equations. Most of these methods are iterative, they produce approximate results that become better and better after each iteration. The problem is that in finance, many competitive financial tools have very close effective rates of return (tools with smaller rates of return are simply not competitive), so to gain profit, we must often operate on a very small difference between different effective rates. Thus, when we select one of the two annuities based on the results q\ and q2 of the computations, we must make be sure that the relation q\ > q2 remains true for the actual (exact) values qi as well. From this viewpoint, it is desirable not just to get an approximate value q, but also get the interval [q, q] that is guaranteed to contain q. In this case, we select the first annuity only if q > q2 this guarantees that q\ > q2. The authors describe techniques for producing such intervals. They also show how these algorithms can be expanded to more complex annuities, e.g., annuities that make payments several times a year.