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Continuous-repayment Mortgage
Analogous to continuous compounding, a continuous annuity is an ordinary annuity in which the payment interval is narrowed indefinitely. A (theoretical) continuous repayment mortgage is a mortgage loan paid by means of a continuous annuity. Mortgages (i.e., mortgage loans) are generally settled over a period of years by a series of fixed regular payments commonly referred to as an annuity. Each payment accumulates compound interest from time of deposit to the end of the mortgage timespan at which point the sum of the payments with their accumulated interest equals the value of the loan with interest compounded over the entire timespan. Given loan ''P''0, per period interest rate i, number of periods ''n'' and fixed per period payment ''x'', the end of term balancing equation is: ::P_0(1+i)^ = \sum_^n x(1+i)^=\frac Summation can be computed using the standard formula for summation of a geometric sequence. In a (theoretical) continuous-repayment mortgage the payment interval ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compound Interest With Varying Frequencies
Compound may refer to: Architecture and built environments * Compound (enclosure), a cluster of buildings having a shared purpose, usually inside a fence or wall ** Compound (fortification), a version of the above fortified with defensive structures * Compound (migrant labour), a hostel for migrant workers such as those historically connected with mines in South Africa * The Compound, an area of Palm Bay, Florida, US * Komboni or compound, a type of slum in Zambia Government and law * Composition (fine), a legal procedure in use after the English Civil War ** Committee for Compounding with Delinquents, an English Civil War institution that allowed Parliament to compound the estates of Royalists * Compounding treason, an offence under the common law of England * Compounding a felony, a previous offense under the common law of England Linguistics * Compound (linguistics), a word that consists of more than one radical element * Compound sentence (linguistics), a type of sentence ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interest Rate Calc Example
In finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distinct from a fee which the borrower may pay the lender or some third party. It is also distinct from dividend which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by risk taking entrepreneurs when the revenue earned exceeds the total costs. For example, a customer would usually pay interest to borrow from a bank, so they pay the bank an amount which is more than the amount they borrowed; or a customer may earn interest on their savings, and so they may withdraw more than they originally deposited. In the case of savings, the customer is the lender, and the bank plays the role of the borrower. Interest diffe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lambert W Function
In mathematics, the Lambert function, also called the omega function or product logarithm, is a multivalued function, namely the Branch point, branches of the converse relation of the function , where is any complex number and is the exponential function. For each integer there is one branch, denoted by , which is a complex-valued function of one complex argument. is known as the principal branch. These functions have the following property: if and are any complex numbers, then :w e^ = z holds if and only if :w=W_k(z) \ \ \text k. When dealing with real numbers only, the two branches and suffice: for real numbers and the equation :y e^ = x can be solved for only if ; we get if and the two values and if . The Lambert relation cannot be expressed in terms of elementary functions. It is useful in combinatorics, for instance, in the enumeration of tree graph, trees. It can be used to solve various equations involving exponentials (e.g. the maxima of the Planck' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton–Raphson
In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function defined for a real variable , the function's derivative , and an initial guess for a root of . If the function satisfies sufficient assumptions and the initial guess is close, then :x_ = x_0 - \frac is a better approximation of the root than . Geometrically, is the intersection of the -axis and the tangent of the graph of at : that is, the improved guess is the unique root of the linear approximation at the initial point. The process is repeated as :x_ = x_n - \frac until a sufficiently precise value is reached. This algorithm is first in the class of Householder's methods, succeeded by Halley's method. The method can also be extended to complex functions an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interest Rate Plot
In finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distinct from a fee which the borrower may pay the lender or some third party. It is also distinct from dividend which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by risk taking entrepreneurs when the revenue earned exceeds the total costs. For example, a customer would usually pay interest to borrow from a bank, so they pay the bank an amount which is more than the amount they borrowed; or a customer may earn interest on their savings, and so they may withdraw more than they originally deposited. In the case of savings, the customer is the lender, and the bank plays the role of the borrower. Interest diffe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perpetuity
A perpetuity is an annuity that has no end, or a stream of cash payments that continues forever. There are few actual perpetuities in existence. For example, the United Kingdom (UK) government issued them in the past; these were known as consols and were all finally redeemed in 2015. Real estate and preferred stock are among some types of investments that affect the results of a perpetuity, and prices can be established using techniques for valuing a perpetuity. Perpetuities are but one of the time value of money methods for valuing financial assets. Perpetuities are a form of ordinary annuities. The concept is closely linked to terminal value and terminal growth rate in valuation. Detailed description A perpetuity is an annuity in which the periodic payments begin on a fixed date and continue indefinitely. It is sometimes referred to as a perpetual annuity. Fixed coupon payments on permanently invested (irredeemable) sums of money are prime examples of perpetuities. Scholar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Difference Equation
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter k that is independent of n; this number k is called the ''order'' of the relation. If the values of the first k numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In ''linear recurrences'', the th term is equated to a linear function of the k previous terms. A famous example is the recurrence for the Fibonacci numbers, F_n=F_+F_ where the order k is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on n. For these recurrences, one can express the general term of the sequence as a closed-form expression of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Constant
In physics and engineering, the time constant, usually denoted by the Greek letter (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system.Concretely, a first-order LTI system is a system that can be modeled by a single first order differential equation in time. Examples include the simplest single-stage electrical RC circuits and RL circuits. The time constant is the main characteristic unit of a first-order LTI system. In the time domain, the usual choice to explore the time response is through the step response to a step input, or the impulse response to a Dirac delta function input. In the frequency domain (for example, looking at the Fourier transform of the step response, or using an input that is a simple sinusoidal function of time) the time constant also determines the bandwidth of a first-order time-invariant system, that is, the frequency at which the output signal power drops to half the value it has at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RC Circuit
A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors. It may be driven by a voltage or current source and these will produce different responses. A first order RC circuit is composed of one resistor and one capacitor and is the simplest type of RC circuit. RC circuits can be used to filter a signal by blocking certain frequencies and passing others. The two most common RC filters are the high-pass filters and low-pass filters; band-pass filters and band-stop filters usually require RLC filters, though crude ones can be made with RC filters. Introduction There are three basic, linear passive lumped analog circuit components: the resistor (R), the capacitor (C), and the inductor (L). These may be combined in the RC circuit, the RL circuit, the LC circuit, and the RLC circuit, with the acronyms indicating which components are used. These circuits, among them, exhibit a large number of important types ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mortgage Balance Model Data
A mortgage loan or simply mortgage (), in civil law jurisdicions known also as a hypothec loan, is a loan used either by purchasers of real property to raise funds to buy real estate, or by existing property owners to raise funds for any purpose while putting a lien on the property being mortgaged. The loan is " secured" on the borrower's property through a process known as mortgage origination. This means that a legal mechanism is put into place which allows the lender to take possession and sell the secured property ("foreclosure" or "repossession") to pay off the loan in the event the borrower defaults on the loan or otherwise fails to abide by its terms. The word ''mortgage'' is derived from a Law French term used in Britain in the Middle Ages meaning "death pledge" and refers to the pledge ending (dying) when either the obligation is fulfilled or the property is taken through foreclosure. A mortgage can also be described as "a borrower giving consideration in the form o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
