The theoretical aspects of mathematical modeling in the banking on the ex ample of compound interest

The compound interest is used in banking. It is one of the ways of establishing the interests (the compound interest), so the fee for the right to have the money at the disposal. It is associated with the multiple calculating of the same percentage from the capital whereby every time the interests are capitalized; they increase the base from which the next percentage is calculated. In this paper are discussed the matters concerning the annual, subperiod and continue capitalization and also associated with them the term of percentage: annual, subperiod, nominal, effective, continuing, and average. The reader will find here the mathematical models enabling to calculate: - the final capital for the initial capital at the given percentage for the fixed time, - the percentage on the basis of the initial and final capital after the established time, - the time of percentage on the basis of initial and final capital after the certain time. The passage of this article concerns the matter of equivalence of the percentage within the time. With the usage of the mathematical models the conditions of equivalence of the percentage were described: the nominal ones (especially subperiod and annual), subperiod and continuing, subperiod and effective, effective and continuing, subperiod and simple percentage. The relationship between the terms is expressed in the form of the mathematical formulas. The presentations of the chosen models on the diagrams or in the tables will ease the reader to understand these terms. The content included in this paper will put the reader flesh on the basics of the theoretical banking calculations in the condition of the compound percentage and it will also show how important in the banking mathematic is.