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Amortization Calculator
An amortization calculator is used to determine the periodic payment amount due on a loan (typically a mortgage), based on the amortization process. The amortization repayment model factors varying amounts of both interest and principal into every installment, though the total amount of each payment is the same. An amortization schedule calculator is often used to adjust the loan amount until the monthly payments will fit comfortably into budget, and can vary the interest rate to see the difference a better rate might make in the kind of home or car one can afford. An amortization calculator can also reveal the exact dollar amount that goes towards interest and the exact dollar amount that goes towards principal out of each individual payment. The amortization schedule is a table delineating these figures across the duration of the loan in chronological order. The formula The calculation used to arrive at the periodic payment amount assumes that the first payment is not due o ...
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Loan
In finance, a loan is the lending of money by one or more individuals, organizations, or other entities to other individuals, organizations, etc. The recipient (i.e., the borrower) incurs a debt and is usually liable to pay interest on that debt until it is repaid as well as to repay the principal amount borrowed. The document evidencing the debt (e.g., a promissory note) will normally specify, among other things, the principal amount of money borrowed, the interest rate the lender is charging, and the date of repayment. A loan entails the reallocation of the subject asset(s) for a period of time, between the lender and the borrower. The interest provides an incentive for the lender to engage in the loan. In a legal loan, each of these obligations and restrictions is enforced by contract, which can also place the borrower under additional restrictions known as loan covenants. Although this article focuses on monetary loans, in practice, any material object might be lent. ...
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Mortgage Loan
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 th ...
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Amortization (business)
In accounting, amortization refers to expensing the acquisition cost minus the residual value of intangible assets in a systematic manner over their estimated "useful economic lives" so as to reflect their consumption, expiry, and obsolescence, or other decline in value as a result of use or the passage of time. The term amortization can also refer to the completion of that process, as in "the amortization of the tower was expected in 1734". Depreciation is a corresponding concept for tangible assets. Methodologies for allocating amortization to each accounting period are generally the same as these for depreciation. However, many intangible assets such as goodwill or certain brands may be deemed to have an indefinite useful life and are therefore not subject to amortization (although goodwill is subjected to an impairment test every year). While theoretically amortization is used to account for the decreasing value of an intangible asset over its useful life, in practice many c ...
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Interest
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 ...
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Amortization Schedule
An amortization schedule is a table detailing each periodic payment on an amortizing loan (typically a mortgage), as generated by an amortization calculator. Amortization refers to the process of paying off a debt (often from a loan or mortgage) over time through regular payments. A portion of each payment is for interest while the remaining amount is applied towards the principal balance. The percentage of interest versus principal in each payment is determined in an amortization schedule. The schedule differentiates the portion of payment that belongs to interest expense from the portion used to close the gap of a discount or premium from the principal after each payment. While a portion of every payment is applied towards both the interest and the principal balance of the loan, the exact amount applied to principal each time varies (with the remainder going to interest). An amortization schedule indicates the specific monetary amount put towards interest, as well as the specific ...
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Root-finding Algorithm
In mathematics and computing, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function , from the real numbers to real numbers or from the complex numbers to the complex numbers, is a number such that . As, generally, the zeros of a function cannot be computed exactly nor expressed in closed form, root-finding algorithms provide approximations to zeros, expressed either as floating-point numbers or as small isolating intervals, or disks for complex roots (an interval or disk output being equivalent to an approximate output together with an error bound). Solving an equation is the same as finding the roots of the function . Thus root-finding algorithms allow solving any equation defined by continuous functions. However, most root-finding algorithms do not guarantee that they will find all the roots; in particular, if such an algorithm does not find any root, that does not mean that no root exists. Most num ...
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Annuity (finance Theory)
In investment, an annuity is a series of payments made at equal intervals.Kellison, Stephen G. (1970). ''The Theory of Interest''. Homewood, Illinois: Richard D. Irwin, Inc. p. 45 Examples of annuities are regular deposits to a savings account, monthly home mortgage payments, monthly insurance payments and pension payments. Annuities can be classified by the frequency of payment dates. The payments (deposits) may be made weekly, monthly, quarterly, yearly, or at any other regular interval of time. Annuities may be calculated by mathematical functions known as "annuity functions". An annuity which provides for payments for the remainder of a person's lifetime is a life annuity. Types Annuities may be classified in several ways. Timing of payments Payments of an ''annuity-immediate'' are made at the end of payment periods, so that interest accrues between the issue of the annuity and the first payment. Payments of an ''annuity-due'' are made at the beginning of payment period ...
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Net (economics)
A net (sometimes written nett) value is the resultant amount after accounting for the sum or difference of two or more variables. In economics, it is frequently used to imply the remaining value after accounting for a specific, commonly understood deduction. In these cases it is contrasted with the term gross, which refers to the pre-deduction value. For example, net income is the total income of a company after deducting its expenses—commonly known as profit—or the total income of an individual after deducting their income tax. Profit may be broken down further into pre-taxed or gross profit and profit after taxes or net profit. Similarly, an individual's net worth is the difference between their assets (what they own) and their liabilities (what they owe to others). Similarly, net investment in physical capital such as machinery equals gross (total) investment minus the dollar amount of replacement investment that offsets depreciation of pre-existing machiner ...
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Annual Percentage Yield
Annual percentage yield (APY) is a normalized representation of an interest rate, based on a compounding period of one year. APY figures allow a reasonable, single-point comparison of different offerings with varying compounding schedules. However, it does not account for the possibility of account fees affecting the net gain. APY generally refers to the rate paid to a depositor by a financial institution, while the analogous annual percentage rate (APR) refers to the rate paid to a financial institution by a borrower. To promote financial products that do not involve debt, banks and other firms will often quote the APY (as opposed to the APR because the APY represents the customer receiving a higher return at the end of the term). For example, a certificate of deposit that has a 4.65% APR, compounded monthly, would instead be quoted as a 4.75% APY. Equation One common mathematical definition of APY uses this effective interest rate formula, but the precise usage may depend on l ...
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Annual Percentage Rate
The term annual percentage rate of charge (APR), corresponding sometimes to a nominal APR and sometimes to an effective APR (EAPR), is the interest rate for a whole year (annualized), rather than just a monthly fee/rate, as applied on a loan, mortgage loan, credit card, etc. It is a finance charge expressed as an annual rate. Those terms have formal, legal definitions in some countries or legal jurisdictions, but in the United States: :* The ''nominal APR'' is the simple-interest rate (for a year). :* The ''effective APR'' is the fee+ compound interest rate (calculated across a year). "Subject: Regulation AA", Alfred F."Bob" Blair, Jr., US Federal Reserve, 2008-06-28, webpage: US-Federal-Reserve-R1314 In some areas, the ''annual percentage rate'' (APR) is the simplified counterpart to the effective interest rate that the borrower will pay on a loan. In many countries and jurisdictions, lenders (such as banks) are required to disclose the "cost" of borrowing in some standa ...
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Geometric Progression
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the ''common ratio''. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2. Examples of a geometric sequence are powers ''r''''k'' of a fixed non-zero number ''r'', such as 2''k'' and 3''k''. The general form of a geometric sequence is :a,\ ar,\ ar^2,\ ar^3,\ ar^4,\ \ldots where ''r'' ≠ 0 is the common ratio and ''a'' ≠ 0 is a scale factor, equal to the sequence's start value. The sum of a geometric progression terms is called a '' geometric series''. Elementary properties The ''n''-th term of a geometric sequence with initial value ''a'' = ''a''1 and common ratio ''r'' is given by :a_n = a\,r^, and in general :a_n = a_m\,r^. Such a geometri ...
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