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 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