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 multiply the PV of an ordinary annuity by (1 + "i"). The following formula use these common variables: The future value ("FV") formula is similar and uses the same variables. The present value formula is the core formula for the time value of money; each of the other formulae is derived from this formula. For example, the annuity formula is the sum of a series of present value calculations. The present value ("PV") formula has four variables, each of which can be solved for by numerical methods: The cumulative present value of future cash flows can be calculated by summing