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120-465: In finance and economics , interest is payment from a debtor 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 to 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
240-788: A loan shark . In many historical societies including ancient Christian, Jewish, and Islamic societies, usury meant the charging of interest of any kind, and was considered wrong, or was made illegal. During the Sutra period in India (7th to 2nd centuries BC) there were laws prohibiting the highest castes from practicing usury. Similar condemnations are found in religious texts from Buddhism, Judaism ( ribbit in Hebrew ), Christianity, and Islam ( riba in Arabic ). At times, many states from ancient Greece to ancient Rome have outlawed loans with any interest. Though
360-441: A "different view". The first written evidence of compound interest dates roughly 2400 BC. The annual interest rate was roughly 20%. Compound interest was necessary for the development of agriculture and important for urbanization. While the traditional Middle Eastern views on interest were the result of the urbanized, economically developed character of the societies that produced them, the new Jewish prohibition on interest showed
480-428: A broad range of subfields exists within finance. Asset- , money- , risk- and investment management aim to maximize value and minimize volatility . Financial analysis assesses the viability, stability, and profitability of an action or entity. Some fields are multidisciplinary, such as mathematical finance , financial law , financial economics , financial engineering and financial technology . These fields are
600-497: A concept is unknown, though its use in Sumeria argue that it was well established as a concept by 3000BC if not earlier, with historians believing that the concept in its modern sense may have arisen from the lease of animal or seeds for productive purposes. The argument that acquired seeds and animals could reproduce themselves was used to justify interest, but ancient Jewish religious prohibitions against usury (נשך NeSheKh ) represented
720-525: A great assembly against them. He that putteth not out his money on interest, nor taketh a bribe against the innocent. He that doeth these things shall never be moved. Johnson contends that the Torah treats lending as philanthropy in a poor community whose aim was collective survival, but which is not obliged to be charitable towards outsiders. A great deal of Jewish legal scholarship in the Early and High Middle Ages
840-424: A growth factor according to the periodic interest, and then decreases by the amount paid p at the end of each period: where By repeated substitution, one obtains expressions for B n , which are linearly proportional to B 0 and p , and use of the formula for the partial sum of a geometric series results in A solution of this expression for p in terms of B 0 and B n reduces to To find
960-431: A high degree of computational complexity and are slow to converge to a solution on classical computers. In particular, when it comes to option pricing, there is additional complexity resulting from the need to respond to quickly changing markets. For example, in order to take advantage of inaccurately priced stock options, the computation must complete before the next change in the almost continuously changing stock market. As
1080-476: A loan is a sin. Usury (in the original sense of any interest) was denounced by religious leaders and philosophers in the ancient world, including Moses , Plato , Aristotle , Cato , Cicero , Seneca , Aquinas , Gautama Buddha and Muhammad . Certain negative historical renditions of usury carry with them social connotations of perceived "unjust" or "discriminatory" lending practices. The historian Paul Johnson comments: Most early religious systems in
1200-470: A loan is considered a form of Tzedakah or Ṣedaqah ( Hebrew : צדקה [ts(e)daˈka] ), a Hebrew word meaning "righteousness" but commonly used to signify charity . (This concept of "charity" differs from the modern Western understanding of "charity". The latter is typically understood as a spontaneous act of goodwill and a marker of generosity; tzedakah is an ethical obligation.) In the Rabbinic period ,
1320-478: A loan or other debt obligations. The main areas of personal finance are considered to be income, spending, saving, investing, and protection. The following steps, as outlined by the Financial Planning Standards Board, suggest that an individual will understand a potentially secure personal finance plan after: Corporate finance deals with the actions that managers take to increase the value of
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#17328513949771440-710: A long-term strategic perspective regarding investment decisions that affect public entities. These long-term strategic periods typically encompass five or more years. Public finance is primarily concerned with: Central banks, such as the Federal Reserve System banks in the United States and the Bank of England in the United Kingdom , are strong players in public finance. They act as lenders of last resort as well as strong influences on monetary and credit conditions in
1560-521: A man wanted to sell wine separately from the use of the wine, he would be selling the same thing twice, or he would be selling what does not exist, wherefore he would evidently commit a sin of injustice." Charles Eisenstein has argued that pivotal change in the English-speaking world came with lawful rights to charge interest on lent money, particularly the 1545 act, "An Act Against Usurie" ( 37 Hen. 8 . c. 9) of King Henry VIII of England. During
1680-414: A mix of an art and science , and there are ongoing related efforts to organize a list of unsolved problems in finance . Managerial finance is the branch of finance that deals with the financial aspects of the management of a company, and the financial dimension of managerial decision-making more broadly. It provides the theoretical underpin for the practice described above , concerning itself with
1800-447: A monthly basis, and the most common rates were multiples of twelve. Monthly rates tended to range from simple fractions to 3–4 percent, perhaps because lenders used Roman numerals . During this period, moneylending primarily involved private loans given to individuals who were consistently in debt or temporarily so until harvest time. This practice was typically carried out by extremely wealthy individuals willing to take on high risks if
1920-445: 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
2040-454: A pastoral, tribal influence. In the early 2nd millennium BC, since silver used in exchange for livestock or grain could not multiply of its own, the Laws of Eshnunna instituted a legal interest rate, specifically on deposits of dowry . Early Muslims called this riba , translated today as the charging of interest. The First Council of Nicaea , in 325, forbade clergy from engaging in usury which
2160-511: A position to take advantage of the situation became the moneylenders when the increasing tax demands in the last declining days of the Empire crippled and eventually destroyed the peasant class by reducing tenant-farmers to serfs . It was evident that usury meant exploitation of the poor. Cicero , in the second book of his treatise De Officiis , relates the following conversation between an unnamed questioner and Cato : ...of whom, when inquiry
2280-447: A result, the finance community is always looking for ways to overcome the resulting performance issues that arise when pricing options. This has led to research that applies alternative computing techniques to finance. Most commonly used quantum financial models are quantum continuous model, quantum binomial model, multi-step quantum binomial model etc. The origin of finance can be traced to the beginning of state formation and trade during
2400-446: A sophisticated mathematical model is required, and thus overlaps several of the above. As a specialized practice area, quantitative finance comprises primarily three sub-disciplines; the underlying theory and techniques are discussed in the next section: DCF valuation formula widely applied in business and finance, since articulated in 1938 . Here, to get the value of the firm , its forecasted free cash flows are discounted to
2520-692: A subject of study, it is related to but distinct from economics , which is the study of the production , distribution , and consumption of goods and services . Based on the scope of financial activities in financial systems , the discipline can be divided into personal , corporate , and public finance . In these financial systems, assets are bought, sold, or traded as financial instruments , such as currencies , loans , bonds , shares , stocks , options , futures , etc. Assets can also be banked , invested , and insured to maximize value and minimize loss. In practice, risks are always present in any financial action and entities. Due to its wide scope,
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#17328513949772640-398: A well-diversified portfolio, achieved investment performance will, in general, largely be a function of the asset mix selected, while the individual securities are less impactful. The specific approach or philosophy will also be significant, depending on the extent to which it is complementary with the market cycle . Risk management here is discussed immediately below. A quantitative fund
2760-482: Is about performing valuation and asset allocation today, based on the risk and uncertainty of future outcomes while appropriately incorporating the time value of money . Determining the present value of these future values, "discounting", must be at the risk-appropriate discount rate , in turn, a major focus of finance-theory. As financial theory has roots in many disciplines, including mathematics, statistics, economics, physics, and psychology, it can be considered
2880-407: Is calculated only on the principal amount, or on that portion of the principal amount that remains. It excludes the effect of compounding . Simple interest can be applied over a time period other than a year, for example, every month. Simple interest is calculated according to the following formula: where For example, imagine that a credit card holder has an outstanding balance of $ 2500 and that
3000-415: Is equal to the interest amount paid or received over a particular period divided by the principal sum borrowed or lent (usually expressed as a percentage). Compound interest means that interest is earned on prior interest in addition to the principal. Due to compounding, the total amount of debt grows exponentially, and its mathematical study led to the discovery of the number e . In practice, interest
3120-459: Is forbidden in both the Old and New Testament. We therefore declare that notorious usurers should not be admitted to communion of the altar or receive christian burial if they die in this sin. Whoever receives them or gives them christian burial should be compelled to give back what he has received, and let him remain suspended from the performance of his office until he has made satisfaction according to
3240-464: Is inherently unjust and one who charges interest sins." Outlawing usury did not prevent investment, but stipulated that in order for the investor to share in the profit he must share the risk. In short he must be a joint-venturer. Simply to invest the money and expect it to be returned regardless of the success of the venture was to make money simply by having money and not by taking any risk or by doing any work or by any effort or sacrifice at all, which
3360-472: Is lent upon interest. Unto a foreigner thou mayest lend upon interest; but unto thy brother thou shalt not lend upon interest; that the L ORD thy God may bless thee in all that thou puttest thy hand unto, in the land whither thou goest in to possess it. that hath withdrawn his hand from the poor, that hath not received interest nor increase, hath executed Mine ordinances, hath walked in My statutes; he shall not die for
3480-436: Is managed using computer-based mathematical techniques (increasingly, machine learning ) instead of human judgment. The actual trading is typically automated via sophisticated algorithms . Risk management , in general, is the study of how to control risks and balance the possibility of gains; it is the process of measuring risk and then developing and implementing strategies to manage that risk. Financial risk management
3600-444: Is mathematics that is actually important in this new scenario Finance theory is heavily based on financial instrument pricing such as stock option pricing. Many of the problems facing the finance community have no known analytical solution. As a result, numerical methods and computer simulations for solving these problems have proliferated. This research area is known as computational finance . Many computational finance problems have
3720-402: Is most often calculated on a daily, monthly, or yearly basis, and its impact is influenced greatly by its compounding rate. Credit is thought to have preceded the existence of coinage by several thousands of years. The first recorded instance of credit is a collection of old Sumerian documents from 3000 BC that show systematic use of credit to loan both grain and metals. The rise of interest as
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3840-657: Is often indirect, through a financial intermediary such as a bank , or via the purchase of notes or bonds ( corporate bonds , government bonds , or mutual bonds) in the bond market . The lender receives interest, the borrower pays a higher interest than the lender receives, and the financial intermediary earns the difference for arranging the loan. A bank aggregates the activities of many borrowers and lenders. A bank accepts deposits from lenders, on which it pays interest. The bank then lends these deposits to borrowers. Banks allow borrowers and lenders, of different sizes, to coordinate their activity. Investing typically entails
3960-408: Is prohibited, as well as making money out of money is unacceptable. All financial transactions must be asset-backed and must not charge any interest or fee for the service of lending. It is thought that Jacob Bernoulli discovered the mathematical constant e by studying a question about compound interest . He realized that if an account that starts with $ 1.00 and pays say 100% interest per year, at
4080-413: Is question of usury. If indeed someone has fallen into the error of presuming to affirm pertinaciously that the practice of usury is not sinful, we decree that he is to be punished as a heretic; and we strictly enjoin on local ordinaries and inquisitors of heresy to proceed against those they find suspect of such error as they would against those suspected of heresy. (canon 29) Up to the 16th century, usury
4200-497: Is referred to as "wholesale finance". Institutions here extend the products offered , with related trading, to include bespoke options , swaps , and structured products , as well as specialized financing ; this " financial engineering " is inherently mathematical , and these institutions are then the major employers of "quants" (see below ). In these institutions, risk management , regulatory capital , and compliance play major roles. As outlined, finance comprises, broadly,
4320-471: Is the branch of economics that studies the interrelation of financial variables , such as prices , interest rates and shares, as opposed to real economic variables, i.e. goods and services . It thus centers on pricing, decision making, and risk management in the financial markets , and produces many of the commonly employed financial models . ( Financial econometrics is the branch of financial economics that uses econometric techniques to parameterize
4440-485: Is the practice of protecting corporate value against financial risks , often by "hedging" exposure to these using financial instruments. The focus is particularly on credit and market risk, and in banks, through regulatory capital, includes operational risk. Financial risk management is related to corporate finance in two ways. Firstly, firm exposure to market risk is a direct result of previous capital investments and funding decisions; while credit risk arises from
4560-400: Is then often referred to as "business finance". Typically, "corporate finance" relates to the long term objective of maximizing the value of the entity's assets , its stock , and its return to shareholders , while also balancing risk and profitability . This entails three primary areas: The latter creates the link with investment banking and securities trading , as above, in that
4680-538: Is usury. St Thomas quotes Aristotle as saying that "to live by usury is exceedingly unnatural". St Thomas allows, however, charges for actual services provided. Thus a banker or credit-lender could charge for such actual work or effort as he did carry out e.g. any fair administrative charges. The Catholic Church, in a decree of the Fifth Council of the Lateran , expressly allowed such charges in respect of credit-unions run for
4800-643: The Bronze Age . The earliest historical evidence of finance is dated to around 3000 BCE. Banking originated in West Asia, where temples and palaces were used as safe places for the storage of valuables. Initially, the only valuable that could be deposited was grain, but cattle and precious materials were eventually included. During the same period, the Sumerian city of Uruk in Mesopotamia supported trade by lending as well as
4920-460: The Catholic Church , argued charging of interest is wrong because it amounts to "double charging", charging for both the thing and the use of the thing. Aquinas said this would be morally wrong in the same way as if one sold a bottle of wine, charged for the bottle of wine, and then charged for the person using the wine to actually drink it. Similarly, one cannot charge for a piece of cake and for
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5040-521: The Lombard bankers and pawnbrokers , who moved from city to city, was along the pilgrim routes. In the 16th century, short-term interest rates dropped dramatically (from around 20–30% p.a. to around 9–10% p.a.). This was caused by refined commercial techniques, increased capital availability, the Reformation , and other reasons. The lower rates weakened religious scruples about lending at interest, although
5160-546: The Mesopotamians , Hittites , Phoenicians and Egyptians , interest was legal and often fixed by the state. But the Hebrew took a different view of the matter. Theological historian John Noonan argues that "the doctrine [of usury] was enunciated by popes, expressed by three ecumenical councils, proclaimed by bishops, and taught unanimously by theologians." In England, the departing Crusaders were joined by crowds of debtors in
5280-486: The Principate period, most banking activities were conducted by private individuals who operated as large banking firms do today. Anybody that had any available liquid assets and wished to lend it out could easily do so. The annual rates of interest on loans varied in the range of 4–12 percent, but when the interest rate was higher, it typically was not 15–16 percent but either 24 percent or 48 percent. They quoted them on
5400-516: The Roman Empire eventually allowed loans with carefully restricted interest rates, the Catholic Church in medieval Europe, as well as the Reformed Churches, regarded the charging of interest at any rate as sinful (as well as charging a fee for the use of money, such as at a bureau de change ). Christian religious prohibitions on usury are predicated upon the belief that charging interest on
5520-548: The Roman Republic , interest was outlawed by the Lex Genucia reforms in 342 BCE, though the provision went largely unenforced. Under Julius Caesar , a ceiling on interest rates of 12% was set, and much later under Justinian it was lowered even further to between 4% and 8%. Usury#Usury in scholastic theology Usury ( / ˈ j uː ʒ ər i / ) is the practice of making loans that are seen as unfairly enriching
5640-446: The managerial application of the various finance techniques . Academics working in this area are typically based in business school finance departments, in accounting , or in management science . The tools addressed and developed relate in the main to managerial accounting and corporate finance : the former allow management to better understand, and hence act on, financial information relating to profitability and performance;
5760-558: The massacres of Jews at London and York in 1189–1190 . In 1275, Edward I of England passed the Statute of the Jewry which made usury illegal and linked it to blasphemy , in order to seize the assets of the violators. Scores of English Jews were arrested, 300 were hanged and their property went to the Crown . In 1290, all Jews were to be expelled from England, allowed to take only what they could carry;
5880-724: The numerical methods applied here. Experimental finance aims to establish different market settings and environments to experimentally observe and provide a lens through which science can analyze agents' behavior and the resulting characteristics of trading flows, information diffusion, and aggregation, price setting mechanisms, and returns processes. Researchers in experimental finance can study to what extent existing financial economics theory makes valid predictions and therefore prove them, as well as attempt to discover new principles on which such theory can be extended and be applied to future financial decisions. Research may proceed by conducting trading simulations or by establishing and studying
6000-526: The theory of fructification . By applying an opportunity cost argument, comparing the loan rate with the rate of return on agricultural land, and a mathematical argument, applying the formula for the value of a perpetuity to a plantation, he argued that the land value would rise without limit, as the interest rate approached zero. For the land value to remain positive and finite keeps the interest rate above zero. Adam Smith , Carl Menger , and Frédéric Bastiat also propounded theories of interest rates. In
6120-408: The $ 6 per year after only 6 months ( time preference ), and so has the opportunity to reinvest the first $ 3 coupon payment after the first 6 months, and earn additional interest. For example, suppose an investor buys $ 10,000 par value of a US dollar bond, which pays coupons twice a year, and that the bond's simple annual coupon rate is 6 percent per year. This means that every 6 months, the issuer pays
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#17328513949776240-529: The Most High; for He is kind to the ungrateful and wicked. Be merciful, just as your Father is merciful. - Luke 6:34-36 NIV The First Council of Nicaea , in 325, forbade clergy from engaging in usury Forasmuch as many enrolled among the Clergy, following covetousness and lust of gain, have forgotten the divine Scripture, which says, " He has not given his money upon usury " [Ezek. xviii, 8], and in lending money ask
6360-478: The above " Fundamental theorem of asset pricing ". The subject has a close relationship with financial economics, which, as outlined, is concerned with much of the underlying theory that is involved in financial mathematics: generally, financial mathematics will derive and extend the mathematical models suggested. Computational finance is the branch of (applied) computer science that deals with problems of practical interest in finance, and especially emphasizes
6480-431: The ancient Near East , and the secular codes arising from them, did not forbid usury. These societies regarded inanimate matter as alive, like plants, animals and people, and capable of reproducing itself. Hence if you lent 'food money', or monetary tokens of any kind, it was legitimate to charge interest. Food money in the shape of olives, dates, seeds or animals was lent out as early as c. 5000 BC, if not earlier. ...Among
6600-462: The appearance of appropriate conditions for entrepreneurs to start new, lucrative businesses. Given that borrowed money was no longer strictly for consumption but for production as well, interest was no longer viewed in the same manner. The first attempt to control interest rates through manipulation of the money supply was made by the Banque de France in 1847. The latter half of the 20th century saw
6720-443: The balances instead of being subtracted, and the formula for the payment is the negative of the one above. These formulas are only approximate since actual loan balances are affected by rounding. To avoid an underpayment at the end of the loan, the payment must be rounded up to the next cent. Finance Finance refers to monetary resources and to the study and discipline of money , currency , assets and liabilities . As
6840-501: The behavior of people in artificial, competitive, market-like settings. Behavioral finance studies how the psychology of investors or managers affects financial decisions and markets and is relevant when making a decision that can impact either negatively or positively on one of their areas. With more in-depth research into behavioral finance, it is possible to bridge what actually happens in financial markets with analysis based on financial theory. Behavioral finance has grown over
6960-450: The benefit of the poor known as " montes pietatis ". In the 13th century Cardinal Hostiensis enumerated thirteen situations in which charging interest was not immoral. The most important of these was lucrum cessans (profits given up) which allowed for the lender to charge interest "to compensate him for profit foregone in investing the money himself." This idea is very similar to opportunity cost. Many scholastic thinkers who argued for
7080-529: The benefit to the borrower, and interest received by the lender in terms of a premium for the risk of default . In the sixteenth century, Martín de Azpilcueta applied a time preference argument: it is preferable to receive a given good now rather than in the future. Accordingly, interest is compensation for the time the lender forgoes the benefit of spending the money. On the question of why interest rates are normally greater than zero, in 1770, French economist Anne-Robert-Jacques Turgot, Baron de Laune proposed
7200-579: The business's credit policy and is often addressed through credit insurance and provisioning . Secondly, both disciplines share the goal of enhancing or at least preserving, the firm's economic value , and in this context overlaps also enterprise risk management , typically the domain of strategic management . Here, businesses devote much time and effort to forecasting , analytics and performance monitoring . (See ALM and treasury management .) For banks and other wholesale institutions, risk management focuses on managing, and as necessary hedging,
7320-891: The capital raised will generically comprise debt, i.e. corporate bonds , and equity , often listed shares . Re risk management within corporates, see below . Financial managers—i.e. as distinct from corporate financiers—focus more on the short term elements of profitability, cash flow, and " working capital management " ( inventory , credit and debtors ), ensuring that the firm can safely and profitably carry out its financial and operational objectives; i.e. that it: (1) can service both maturing short-term debt repayments, and scheduled long-term debt payments, and (2) has sufficient cash flow for ongoing and upcoming operational expenses . (See Financial management and Financial planning and analysis .) Public finance describes finance as related to sovereign states, sub-national entities, and related public entities or agencies. It generally encompasses
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#17328513949777440-499: The capital, a moderate sum for their expenses and by way of compensation, provided it is intended exclusively to defray the expenses of those employed and of other things pertaining (as mentioned) to the upkeep of the organizations, and provided that no profit is made therefrom. They ought not, indeed, to be condemned in any way. Rather, such a type of lending is meritorious and should be praised and approved. It certainly should not be considered as usurious; (...) Pope Sixtus V condemned
7560-434: The case of savings, the customer is the lender, and the bank plays the role of the borrower. Interest differs from profit , in that interest is received by a lender, whereas profit is received by the owner of an asset , investment or enterprise . (Interest may be part or the whole of the profit on an investment , but the two concepts are distinct from each other from an accounting perspective.) The rate of interest
7680-460: The debate did not cease altogether. The 18th century papal prohibition on usury meant that it was a sin to charge interest on a money loan. As set forth by Thomas Aquinas in the 13th century, because money was invented to be an intermediary in exchange for goods, it is unjust to charge a fee to someone after giving them money. This is because transferring ownership of property implies the right to use that property for its purpose: "Accordingly if
7800-451: The eating of the piece of cake. Yet this, said Aquinas, is what usury does. Money is a medium of exchange, and is used up when it is spent. To charge for the money and for its use (by spending) is therefore to charge for the money twice. It is also to sell time since the usurer charges, in effect, for the time that the money is in the hands of the borrower. Time, however, is not a commodity for which anyone can charge. In condemning usury Aquinas
7920-461: The economy. Development finance , which is related, concerns investment in economic development projects provided by a (quasi) governmental institution on a non-commercial basis; these projects would otherwise not be able to get financing . A public–private partnership is primarily used for infrastructure projects: a private sector corporate provides the financing up-front, and then draws profits from taxpayers or users. Climate finance , and
8040-400: The end of the year, the value is $ 2.00; but if the interest is computed and added twice in the year, the $ 1 is multiplied by 1.5 twice, yielding $ 1.00×1.5 = $ 2.25. Bernoulli noticed that if the frequency of compounding is increased without limit, this sequence can be modeled as follows: where n is the number of times the interest is to be compounded in a year. In economics,
8160-672: The excess, intending to earn a fair return. Correspondingly, an entity where income is less than expenditure can raise capital usually in one of two ways: (i) by borrowing in the form of a loan (private individuals), or by selling government or corporate bonds ; (ii) by a corporation selling equity , also called stock or shares (which may take various forms: preferred stock or common stock ). The owners of both bonds and stock may be institutional investors —financial institutions such as investment banks and pension funds —or private individuals, called private investors or retail investors. (See Financial market participants .) The lending
8280-510: The field is referred to as quantitative finance and / or mathematical finance, and comprises primarily the three areas discussed. The main mathematical tools and techniques are, correspondingly: Mathematically, these separate into two analytic branches : derivatives pricing uses risk-neutral probability (or arbitrage-pricing probability), denoted by "Q"; while risk and portfolio management generally use physical (or actual or actuarial) probability, denoted by "P". These are interrelated through
8400-416: The field. Quantum finance is an interdisciplinary field, in which theories and methods developed by quantum physicists and economists are applied to solve financial problems. It represents a branch known as econophysics. Although quantum computational methods have been around for quite some time and use the basic principles of physics to better understand the ways to implement and manage cash flows, it
8520-410: The firm to the shareholders, the sources of funding and the capital structure of corporations, and the tools and analysis used to allocate financial resources. While corporate finance is in principle different from managerial finance , which studies the financial management of all firms rather than corporations alone, the concepts are applicable to the financial problems of all firms, and this area
8640-451: The first scholarly work in this area. The field is largely focused on the modeling of derivatives —with much emphasis on interest rate- and credit risk modeling —while other important areas include insurance mathematics and quantitative portfolio management . Relatedly, the techniques developed are applied to pricing and hedging a wide range of asset-backed , government , and corporate -securities. As above , in terms of practice,
8760-627: The flows of capital that take place between individuals and households ( personal finance ), governments ( public finance ), and businesses ( corporate finance ). "Finance" thus studies the process of channeling money from savers and investors to entities that need it. Savers and investors have money available which could earn interest or dividends if put to productive use. Individuals, companies and governments must obtain money from some external source, such as loans or credit, when they lack sufficient funds to run their operations. In general, an entity whose income exceeds its expenditure can lend or invest
8880-400: The foundation of business and accounting . In some cases, theories in finance can be tested using the scientific method , covered by experimental finance . The early history of finance parallels the early history of money , which is prehistoric . Ancient and medieval civilizations incorporated basic functions of finance, such as banking, trading and accounting, into their economies. In
9000-708: The fundamental risk mitigant here, investment managers will apply various hedging techniques as appropriate, these may relate to the portfolio as a whole or to individual stocks . Bond portfolios are often (instead) managed via cash flow matching or immunization , while for derivative portfolios and positions, traders use "the Greeks" to measure and then offset sensitivities. In parallel, managers — active and passive — will monitor tracking error , thereby minimizing and preempting any underperformance vs their "benchmark" . Quantitative finance—also referred to as "mathematical finance"—includes those finance activities where
9120-569: The hated trade of moneylending. Several historical rulings in Jewish law have mitigated the allowances for usury toward non-Jews. For instance, the 15th-century commentator Rabbi Isaac Abarbanel specified that the rubric for allowing interest does not apply to Christians or Muslims, because their faith systems have a common ethical basis originating from Judaism. The medieval commentator Rabbi David Kimhi extended this principle to non-Jews who show consideration for Jews, saying they should be treated with
9240-506: The heart of investment management is asset allocation — diversifying the exposure among these asset classes , and among individual securities within each asset class—as appropriate to the client's investment policy , in turn, a function of risk profile, investment goals, and investment horizon (see Investor profile ). Here: Overlaid is the portfolio manager's investment style —broadly, active vs passive , value vs growth , and small cap vs. large cap —and investment strategy . In
9360-403: The holder of the bond a coupon of 3 dollars per 100 dollars par value. At the end of 6 months, the issuer pays the holder: Assuming the market price of the bond is 100, so it is trading at par value, suppose further that the holder immediately reinvests the coupon by spending it on another $ 300 par value of the bond. In total, the investor therefore now holds: and so earns a coupon at the end of
9480-438: The hundredth of the sum [as monthly interest], the holy and great Synod thinks it just that if after this decree any one be found to receive usury, whether he accomplish it by secret transaction or otherwise, as by demanding the whole and one half, or by using any other contrivance whatever for filthy lucre's sake, he shall be deposed from the clergy and his name stricken from the list. (canon 17). [bracketed material in source] At
9600-450: The iniquity of his father, he shall surely live. In thee have they taken gifts to shed blood; thou hast taken interest and increase, and thou hast greedily gained of thy neighbours by oppression, and hast forgotten Me, saith the Lord GOD. Then I consulted with myself, and contended with the nobles and the rulers, and said unto them: 'Ye lend upon pledge, every one to his brother.' And I held
9720-607: The judgment of his own bishop. (canon 25) [emphasis in source] The Council of Vienne made the belief in the right to usury a heresy in 1311, and condemned all secular legislation that allowed it. Serious suggestions have been made to us that communities in certain places, to the divine displeasure and injury of the neighbour, in violation of both divine and human law, approve of usury. By their statutes, sometimes confirmed by oath, they not only grant that usury may be demanded and paid, but deliberately compel debtors to pay it. By these statutes they impose heavy burdens on those claiming
9840-444: The last few decades to become an integral aspect of finance. Behavioral finance includes such topics as: A strand of behavioral finance has been dubbed quantitative behavioral finance , which uses mathematical and statistical methodology to understand behavioral biases in conjunction with valuation. Quantum finance involves applying quantum mechanical approaches to financial theory, providing novel methods and perspectives in
9960-478: The late 19th century, Swedish economist Knut Wicksell in his 1898 Interest and Prices elaborated a comprehensive theory of economic crises based upon a distinction between natural and nominal interest rates . In the 1930s, Wicksell's approach was refined by Bertil Ohlin and Dennis Robertson and became known as the loanable funds theory. Other notable interest rate theories of the period are those of Irving Fisher and John Maynard Keynes . Simple interest
10080-423: The late 19th century, the global financial system was formed. In the middle of the 20th century, finance emerged as a distinct academic discipline, separate from economics. The earliest doctoral programs in finance were established in the 1960s and 1970s. Today, finance is also widely studied through career -focused undergraduate and master's level programs. As outlined, the financial system consists of
10200-427: The latter, as above, are about optimizing the overall financial structure, including its impact on working capital. Key aspects of managerial finance thus include: The discussion, however, extends to business strategy more broadly, emphasizing alignment with the company's overall strategic objectives; and similarly incorporates the managerial perspectives of planning, directing, and controlling. Financial economics
10320-442: The lender. The term may be used in a moral sense—condemning taking advantage of others' misfortunes—or in a legal sense, where an interest rate is charged in excess of the maximum rate that is allowed by law. A loan may be considered usurious because of excessive or abusive interest rates or other factors defined by the laws of a state. Someone who practices usury can be called a usurer , but in modern colloquial English may be called
10440-417: The nearest cent.) Compound interest includes interest earned on the interest that was previously accumulated. Compare, for example, a bond paying 6 percent semiannually (that is, coupons of 3 percent twice a year) with a certificate of deposit ( GIC ) that pays 6 percent interest once a year. The total interest payment is $ 6 per $ 100 par value in both cases, but the holder of the semiannual bond receives half
10560-445: The next 6 months of: Assuming the bond remains priced at par, the investor accumulates at the end of a full 12 months a total value of: and the investor earned in total: The formula for the annual equivalent compound interest rate is: where For example, in the case of a 6% simple annual rate, the annual equivalent compound rate is: The outstanding balance B n of a loan after n regular payments increases each period by
10680-406: The payment if the loan is to be finished in n payments, one sets B n = 0. The PMT function found in spreadsheet programs can be used to calculate the monthly payment of a loan: An interest-only payment on the current balance would be The total interest, I T , paid on the loan is The formulas for a regular savings program are similar, but the payments are added to
10800-423: The potential profit seemed promising. Interest rates were set privately and were largely unrestricted by law. Investment was always regarded as a matter of seeking personal profit, often on a large scale. Banking was of the small, back-street variety, run by the urban lower-middle class of petty shopkeepers. By the 3rd century, acute currency problems in the Empire drove such banking into decline. The rich who were in
10920-408: The practice of charging interest as "detestable to God and man, damned by the sacred canons, and contrary to Christian charity. The first of the scholastic Christian theologians, Saint Anselm of Canterbury , led the shift in thought that labelled charging interest the same as theft. Previously usury had been seen as a lack of charity . St. Thomas Aquinas , the leading scholastic theologian of
11040-486: The practice of charging interest to non-Jews has been restricted to cases when there is no other means of subsistence. "If we nowadays allow interest to be taken from non-Jews, it is because there is no end to the yoke and the burden king and ministers impose on us, and everything we take is the minimum for our subsistence, and anyhow we are condemned to live in the midst of the nations and cannot earn our living in any other manner except by money dealings with them; therefore
11160-444: The present using the weighted average cost of capital for the discount factor. For share valuation investors use the related dividend discount model . Financial theory is studied and developed within the disciplines of management , (financial) economics , accountancy and applied mathematics . Abstractly, finance is concerned with the investment and deployment of assets and liabilities over "space and time"; i.e., it
11280-409: The purchase of stock , either individual securities or via a mutual fund , for example. Stocks are usually sold by corporations to investors so as to raise required capital in the form of " equity financing ", as distinct from the debt financing described above. The financial intermediaries here are the investment banks . The investment banks find the initial investors and facilitate the listing of
11400-728: The rate of 20 percent per year. By 1200 BCE, cowrie shells were used as a form of money in China . The use of coins as a means of representing money began in the years between 700 and 500 BCE. Herodotus mentions the use of crude coins in Lydia around 687 BCE and, by 640 BCE, the Lydians had started to use coin money more widely and opened permanent retail shops. Shortly after, cities in Classical Greece , such as Aegina , Athens , and Corinth , started minting their own coins between 595 and 570 BCE. During
11520-500: The rate of interest is the price of credit , and it plays the role of the cost of capital . In a free market economy, interest rates are subject to the law of supply and demand of the money supply , and one explanation of the tendency of interest rates to be generally greater than zero is the scarcity of loanable funds . Over centuries, various schools of thought have developed explanations of interest and interest rates. The School of Salamanca justified paying interest in terms of
11640-724: The related Environmental finance , address the financial strategies, resources and instruments used in climate change mitigation . Investment management is the professional asset management of various securities—typically shares and bonds, but also other assets, such as real estate, commodities and alternative investments —in order to meet specified investment goals for the benefit of investors. As above, investors may be institutions, such as insurance companies, pension funds, corporations, charities, educational establishments, or private investors, either directly via investment contracts or, more commonly, via collective investment schemes like mutual funds, exchange-traded funds , or REITs . At
11760-413: The relationships suggested.) The discipline has two main areas of focus: asset pricing and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital; respectively: Financial mathematics is the field of applied mathematics concerned with financial markets ; Louis Bachelier's doctoral thesis , defended in 1900, is considered to be
11880-482: The rest of their property became the Crown's. Usury was cited as the official reason for the Edict of Expulsion ; however, not all Jews were expelled: it was easy to avoid expulsion by converting to Christianity. Many other crowned heads of Europe expelled Jewish people, although again converts to Christianity were no longer considered Jewish. Many of these forced converts still secretly practiced their faith. The growth of
12000-516: The return of usurious payments, employing also various pretexts and ingenious frauds to hinder the return. We, therefore, wishing to get rid of these pernicious practices, decree with the approval of the sacred council that all the magistrates, captains, rulers, consuls, judges, counsellors or any other officials of these communities who presume in the future to make, write or dictate such statutes, or knowingly decide that usury be paid or, if paid, that it be not fully and freely restored when claimed, incur
12120-435: The rise of interest-free Islamic banking and finance , a movement that applies Islamic law to financial institutions and the economy. Some countries, including Iran, Sudan, and Pakistan, have taken steps to eradicate interest from their financial systems. Rather than charging interest, the interest-free lender shares the risk by investing as a partner in profit loss sharing scheme, because predetermined loan repayment as interest
12240-408: The same consideration when they borrow. The Old Testament "condemns the practice of charging interest on a poor person because a loan should be an act of compassion and taking care of one’s neighbor"; it teaches that "making a profit off a loan from a poor person is exploiting that person (Exodus 22:25–27)." Similarly, charging of interest ( Hebrew : נֶֽשֶׁךְ , romanized : nešeḵ ) or
12360-568: The same declaration, gave explicit approval of charging a fee for services so long as no profit was made in the case of Mounts of Piety : (...) We declare and define, with the approval of the Sacred Council, that the above-mentioned credit organisations, established by states and hitherto approved and confirmed by the authority of the Apostolic See, do not introduce any kind of evil or provide any incentive to sin if they receive, in addition to
12480-631: The same reason, interest has often been looked down upon in Islamic civilization , with almost all scholars agreeing that the Qur'an explicitly forbids charging interest. Medieval jurists developed several financial instruments to encourage responsible lending and circumvent prohibitions on usury, such as the Contractum trinius . In the Renaissance era, greater mobility of people facilitated an increase in commerce and
12600-475: The securities, typically shares and bonds. Additionally, they facilitate the securities exchanges , which allow their trade thereafter, as well as the various service providers which manage the performance or risk of these investments. These latter include mutual funds , pension funds , wealth managers , and stock brokers , typically servicing retail investors (private individuals). Inter-institutional trade and investment, and fund-management at this scale ,
12720-548: The sentence of excommunication. They shall also incur the same sentence unless within three months they delete from the books of their communities, if they have the power, statutes of this kind hitherto published, or if they presume to observe in any way these statutes or customs. Furthermore, since money-lenders for the most part enter into usurious contracts so frequently with secrecy and guile that they can be convicted only with difficulty, we decree that they be compelled by ecclesiastical censure to open their account books, when there
12840-490: The simple annual interest rate is 12.99% per annum , applied monthly, so the frequency of applying interest is 12 per year. Over one month, interest is due (rounded to the nearest cent). Simple interest applied over 3 months would be If the card holder pays off only interest at the end of each of the 3 months, the total amount of interest paid would be which is the simple interest applied over 3 months, as calculated above. (The one cent difference arises due to rounding to
12960-637: The taking of clothing as pledges is condemned in Ezekiel 18 (early 6th century BC), and Deuteronomy 23:19 prohibits the taking of interest in the form of money or food when lending to a "brother". The New Testament likewise teaches giving rather than loaning money to those who need it: "And if you lend to those from whom you expect repayment, what credit is that to you? Even sinners lend to sinners, expecting to be repaid in full. But love your enemies, do good to them, and lend to them, expecting nothing in return. Then your reward will be great, and you will be sons of
13080-662: The taking of interest is not to be prohibited" (Tos. to BM 70b S.V. tashikh). This is outlined in the Jewish scriptures , specifically in the Torah : If thou lend money to any of My people, even to the poor with thee, thou shalt not be to him as a creditor; neither shall ye lay upon him interest. Take thou no interest of him or increase; but fear thy God; that thy brother may live with thee. Thou shalt not give him thy money upon interest, nor give him thy victuals for increase. Thou shalt not lend upon interest to thy brother: interest of money, interest of victuals, interest of any thing that
13200-463: The thing and the use of the thing. In the medieval economy , loans were entirely a consequence of necessity (bad harvests, fire in a workplace) and, under those conditions, it was considered morally reproachable to charge interest. It was also considered morally dubious, since no goods were produced through the lending of money, and thus it should not be compensated, unlike other activities with direct physical output such as blacksmithing or farming. For
13320-623: The three areas of personal finance, corporate finance, and public finance. These, in turn, overlap and employ various activities and sub-disciplines—chiefly investments , risk management, and quantitative finance . Personal finance refers to the practice of budgeting to ensure enough funds are available to meet basic needs, while ensuring there is only a reasonable level of risk to lose said capital. Personal finance may involve paying for education, financing durable goods such as real estate and cars, buying insurance , investing, and saving for retirement . Personal finance may also involve paying for
13440-516: The time, usury was interest of any kind, and the canon forbade the clergy to lend money at interest rates even as low as 1 percent per year. Later ecumenical councils applied this regulation to the laity . Lateran III decreed that persons who accepted interest on loans could receive neither the sacraments nor Christian burial. Nearly everywhere the crime of usury has become so firmly rooted that many, omitting other business, practise usury as if it were permitted, and in no way observe how it
13560-587: The unpopularity—and so, of course, the pressure—would increase. Thus the Jews became an element in a vicious circle. The Christians, on the basis of the Biblical rulings, condemned interest-taking absolutely, and from 1179 those who practiced it were excommunicated . Catholic autocrats frequently imposed the harshest financial burdens on the Jews. The Jews reacted by engaging in the one business where Christian laws actually discriminated in their favor, and became identified with
13680-446: The use of interest. In Sumerian, "interest" was mas , which translates to "calf". In Greece and Egypt, the words used for interest, tokos and ms respectively, meant "to give birth". In these cultures, interest indicated a valuable increase, and seemed to consider it from the lender's point of view. The Code of Hammurabi (1792–1750 BCE) included laws governing banking operations. The Babylonians were accustomed to charging interest at
13800-635: The various positions held by the institution—both trading positions and long term exposures —and on calculating and monitoring the resultant economic capital , and regulatory capital under Basel III . The calculations here are mathematically sophisticated, and within the domain of quantitative finance as below. Credit risk is inherent in the business of banking, but additionally, these institutions are exposed to counterparty credit risk . Banks typically employ Middle office "Risk Groups" , whereas front office risk teams provide risk "services" (or "solutions") to customers. Additional to diversification ,
13920-583: Was condemned by the Catholic Church, but not really defined. During the Fifth Lateran Council , in the 10th session (in the year 1515), the Council for the first time gave a definition of usury: For, that is the real meaning of usury: when, from its use, a thing which produces nothing is applied to the acquiring of gain and profit without any work, any expense or any risk. The Fifth Lateran Council, in
14040-515: Was defined as lending on interest above 1 percent per month (12.7% AER ). Ninth-century ecumenical councils applied this regulation to the laity . Catholic Church opposition to interest hardened in the era of the Scholastics , when even defending it was considered a heresy . St. Thomas Aquinas , the leading theologian of the Catholic Church , argued that the charging of interest is wrong because it amounts to " double charging ", charging for both
14160-705: Was devoted to making business dealings fair, honest and efficient. As Jewish people were ostracized from most professions by local rulers during the Middle Ages, the Western churches and the guilds , they were pushed into marginal occupations considered socially inferior, such as tax and rent collecting and moneylending. Natural tensions between creditors and debtors were added to social, political, religious, and economic strains. ...financial oppression of Jews tended to occur in areas where they were most disliked, and if Jews reacted by concentrating on moneylending to non-Jews,
14280-449: Was made, what was the best policy in the management of one's property, he answered "Good grazing." "What was next?" "Tolerable grazing." "What third?" "Bad grazing." "What fourth?" "Tilling." And when he who had interrogated him inquired, "What do you think of lending at usury?" Then Cato answered, "What do you think of murder?" The book of Deuteronomy prohibits Jews from charging interest except when making loans to foreigners. Typically,
14400-598: Was much influenced by the recently rediscovered philosophical writings of Aristotle and his desire to assimilate Greek philosophy with Christian theology . Aquinas argued that in the case of usury, as in other aspects of Christian revelation, Christian doctrine is reinforced by Aristotelian natural law rationalism. Aristotle's argument is that interest is unnatural, since money, as a sterile element, cannot naturally reproduce itself. Thus, usury conflicts with natural law just as it offends Christian revelation: see Thought of Thomas Aquinas . As such, Aquinas taught "that interest
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