Longa (music) Longa (music) A longa (pl. "longe" or "longae"), long, quadruple note (Am.), or quadruple whole note is a musical note that could be either twice or three times as long as a breve (Am.: double whole note, or double note), four or six times as long as a semibreve (Am.: whole note), that appears in early music. The number of breves in a long was determined by the "modus" or "mode" of a passage. Sections in perfect mode used three breves to the long while sections in imperfect mode used two breves to the long. Imperfect longs, worth two breves,
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