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 can be computed as that whose interest equals the annuity payment amount: Note that no money enters or leaves the combined system of endowment principal + accumulated annuity payments, and thus the future value of this system can be computed simply via the future value formula: Initially, before any payments, the present value of the system is just the endowment principal (formula_24). At the end, the future value is the endowment principal (which is the same) plus the future value of the total annuity payments (formula_25). Plugging this back into the equation: Without showing the formal derivation here, the perpetuity