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 at future time "n": Summing over all payments from time 1 to time n, then reversing t Note that this is a geometric series, with the initial value being "a" = "C", the multiplicative factor being 1 + "i", with "n" terms. Applying the formula for geometric series, we get The present value of the annuity (PVA) is obtained by simply dividing by formula_19: Another simple and intuitive way to derive the future value of an annuity is to consider an endowment, whose interest is paid as the annuity, and whose principal remains constant. The principal of this hypothetical endowment