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In finance, the rule of 72, the rule of 70 [1] 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.
Trachtenberg called this the 2 Finger Method. The calculations for finding the fourth digit from the example above are illustrated at right. The arrow from the nine will always point to the digit of the multiplicand directly above the digit of the answer you wish to find, with the other arrows each pointing one digit to the right.
The greedy method, and extensions of it for the approximation of irrational numbers, have been rediscovered several times by modern mathematicians, [3] earliest and most notably by J. J. Sylvester [4] A closely related expansion method that produces closer approximations at each step by allowing some unit fractions in the sum to be negative ...
A refinement of the simple Dietz method is the modified Dietz method, [3] which takes available information on the actual timing of external flows into consideration. Like the modified Dietz method, the simple Dietz method is based on the assumption of a simple rate of return principle, unlike the internal rate of return method, which applies a ...
The modified Dietz method [1] [2] [3] is a measure of the ex post (i.e. historical) performance of an investment portfolio in the presence of external flows. (External flows are movements of value such as transfers of cash, securities or other instruments in or out of the portfolio, with no equal simultaneous movement of value in the opposite direction, and which are not income from the ...
The simplex method is remarkably efficient in practice and was a great improvement over earlier methods such as Fourier–Motzkin elimination. However, in 1972, Klee and Minty [ 32 ] gave an example, the Klee–Minty cube , showing that the worst-case complexity of simplex method as formulated by Dantzig is exponential time .
This method was explained by Rashi, [32] (b. Sukkah 45a), [33] as well as in Sefer HaBahir (c. 1150~1200). [34] Kabbalist legends state that the 72-fold name was used by Moses to cross the Red Sea, and that it could grant later holy men the power to cast out demons, heal the sick, prevent natural disasters, and even kill enemies. [29]
Horner's method is a fast, code-efficient method for multiplication and division of binary numbers on a microcontroller with no hardware multiplier. One of the binary numbers to be multiplied is represented as a trivial polynomial, where (using the above notation) a i = 1 {\displaystyle a_{i}=1} , and x = 2 {\displaystyle x=2} .