Music of the Trecento system of division of the breve into 2, 3, 4, 6,8, 9, or 12 semibreves (later minims) with dots (singular "punctus divisionis") indicating breaks at the end of a breve (however, Marchetto never used a term 'punctus divisionis'). Although more Trecento music is written in the international system of notation descended from Franco of Cologne and Philippe de Vitry than in the Marchettian system (and there exist a few, mostly instrumental, works not of Italian origin that use this system), nonetheless, Marchetto's contribution to rhythmic notation is so connected with the Italian Trecento that it is often referred to as
Time value of money not already occurred), or simply not define the value at that point. In case the discount rate is constant, formula_47 this simplifies to where formula_49 is "time remaining until cash flow". Thus for a stream of cash flows "f"("u") ending by time "T" (which can be set to formula_50 for no time horizon) the value at time "t," formula_51 is given by combining the values of these individual cash flows: This formalizes time value of money to future values of cash flows with varying discount rates, and is the basis of many formulas in financial mathematics, such as the Black–Scholes