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Anatocism
Compound interest is interest accumulated from a principal sum and previously accumulated interest. It is the result of reinvesting or retaining interest that would otherwise be paid out, or of the accumulation of debts from a borrower. Compound interest is contrasted with simple interest, where previously accumulated interest is not added to the principal amount of the current period. Compounded interest depends on the simple interest rate applied and the frequency at which the interest is compounded. Compounding frequency The ''compounding frequency'' is the number of times per given unit of time the accumulated interest is capitalized, on a regular basis. The frequency could be yearly, half-yearly, quarterly, monthly, weekly, daily, continuously, or not at all until maturity. For example, monthly capitalization with interest expressed as an annual rate means that the compounding frequency is 12, with time periods measured in months. Annual equivalent rate To help consum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Itô Calculus
Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process). It has important applications in mathematical finance and stochastic differential equations. The central concept is the Itô stochastic integral, a stochastic generalization of the Riemann–Stieltjes integral in analysis. The integrands and the integrators are now stochastic processes: Y_t = \int_0^t H_s\,dX_s, where is a locally square-integrable process adapted to the filtration generated by , which is a Brownian motion or, more generally, a semimartingale. The result of the integration is then another stochastic process. Concretely, the integral from 0 to any particular is a random variable, defined as a limit of a certain sequence of random variables. The paths of Brownian motion fail to satisfy the requirements to be able to apply the standard techniques of calculus. So with the integrand a stochastic process, the Itô stochas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
E (mathematical Constant)
The number is a mathematical constant approximately equal to 2.71828 that is the base of a logarithm, base of the natural logarithm and exponential function. It is sometimes called Euler's number, after the Swiss mathematician Leonhard Euler, though this can invite confusion with Euler numbers, or with Euler's constant, a different constant typically denoted \gamma. Alternatively, can be called Napier's constant after John Napier. The Swiss mathematician Jacob Bernoulli discovered the constant while studying compound interest. The number is of great importance in mathematics, alongside 0, 1, Pi, , and . All five appear in one formulation of Euler's identity e^+1=0 and play important and recurring roles across mathematics. Like the constant , is Irrational number, irrational, meaning that it cannot be represented as a ratio of integers, and moreover it is Transcendental number, transcendental, meaning that it is not a root of any non-zero polynomial with rational coefficie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacob Bernoulli
Jacob Bernoulli (also known as James in English or Jacques in French; – 16 August 1705) was a Swiss mathematician. He sided with Gottfried Wilhelm Leibniz during the Leibniz–Newton calculus controversy and was an early proponent of Leibnizian calculus, to which he made numerous contributions. A member of the Bernoulli family, he, along with his brother Johann, was one of the founders of the calculus of variations. He also discovered the fundamental mathematical constant . However, his most important contribution was in the field of probability, where he derived the first version of the law of large numbers in his work '' Ars Conjectandi''.Jacob (Jacques) Bernoulli [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule Of 72
In finance, the rule of 72, the rule of 70 and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate number of periods required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available. These rules apply to exponential growth and are therefore used for compound interest as opposed to simple interest calculations. They can also be used for decay to obtain a halving time. The choice of number is mostly a matter of preference: 69 is more accurate for continuous compounding, while 72 works well in common interest situations and is more easily divisible. There are a number of variations to the rules that improve accuracy. For periodic compounding, the ''exact'' doubling time for an interes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Luca Pacioli
Luca Bartolomeo de Pacioli, O.F.M. (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting. He is referred to as the father of accounting and bookkeeping and he was the first person to publish a work on the double-entry system of book-keeping on the continent. He was also called Luca di Borgo after his birthplace, Borgo Sansepolcro, Tuscany. Life Luca Pacioli was born between 1446 and 1448 in the Tuscan town of Sansepolcro where he received an abbaco education. This was education in the vernacular (''i.e.'', the local tongue) rather than Latin and focused on the knowledge required of merchants. His father was Bartolomeo Pacioli; however, Luca Pacioli was said to have lived with the Befolci family as a child in his birth town Sansepolcro. He moved to Venice around 1464, where he continued his own education while working ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Summa De Arithmetica
Summa and its diminutive summula (plural ''summae'' and ''summulae'', respectively) was a medieval didactics literary genre written in Latin, born during the 12th century, and popularized in 13th century Europe. In its simplest sense, they might be considered texts that 'sum up' knowledge in a field, such as the compendiums of theology, philosophy and canon law. Their function during the Middle Ages was largely as manuals or handbooks of necessary knowledge used by individuals who would not advance their studies any further. Features It was a kind of encyclopedia that developed a matter about Law, Theology or Philosophy most of all. Matters were divided in a more detailed way as it was in the ''tractatus'' ( treatise), since they were divided into ''quaestiones'' (questions) and these ones were also divided into ''articles''. The articles had the following structure: #Title of the article as a question and showing two different positions (''disputatio''). #Objections or argumen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pratica Della Mercatura
The ''Practica della mercatura'' (Italian for "The Practice of Commerce"),. also known as the ''Merchant's Handbook'', is a comprehensive guide to international trade in 14th-century Eurasia and North Africa as known to its compiler, the Florentine banker Francesco Balducci Pegolotti. It was written sometime between 1335 and 1343, the most likely dates being 1339 or 1340. Its original title was the ''Book of Descriptions of Lands'' ('); its more common name is that from its first printing in 1766. Pegolotti's work is based on his own experience as a banker and merchant for the Bardi, and on various local documents, statutes and price lists available to him. History No autograph survives. The sole surviving manuscript, used by all the printed editions, is that in the Biblioteca Riccardiana at Florence. It states that it was copied on 19 March 1472 by Filippo di Niccolaio Frescobaldi from a copy held by Agnolo di Lotti of Anella, who claimed it had been made from Pegolotti's origi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
