Mensural notation recoverable from the modern text. While 19th and early 20th century editions of Renaissance music often preserved the large note values of the originals, including breves and longs, most modern editions will use scaled-down note values in order to match modern reading habits regarding tempo and beat structure. For 16th century music, a frequent scheme is diminution by a factor of 2 (i.e., rendering semibreves as modern minims), in a modern "alla breve" bar. Older music might be diminished by a factor of 4 (rendering semibreves as crotchets) or sometimes 8 (rendering breves as crotchets). For 13th-century pieces, diminution by
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