# Essays in the theory of risk bearing

## Essays in the Theory of Risk-bearing (Markham Economics

The lender may want to cover his maximum risk, but lenders with portfolios of debt can lower the risk premium to cover just the most probable outcome. Composition of interest rates edit In economics, interest is considered the price of credit, therefore, it is also subject to distortions due to inflation. The nominal interest rate, which refers to the price before adjustment to inflation, is the one visible to the consumer (i.e., the interest tagged in a loan contract, credit card statement, etc.). Nominal interest is composed of the real interest rate plus inflation, among other factors. An approximate formula for the nominal interest is: irπdisplaystyle irpi where i is the nominal interest rate r is the real interest rate and π is inflation. See also: Fisher equation However, not all borrowers and lenders have access to the same interest rate, even if they are subject to the same inflation.

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Allow the interest rate to be advertising periodically changed. While a "fixed interest rate" remains the same throughout the life of the debt, "variable" or "floating" rates can be reset. There are derivative products that allow for hedging and swaps between the two. However interest rates are set by the market, and it happens frequently that they are insufficient to compensate for inflation: for example at times of high inflation during,. G., the oil crisis; and currently (2011) when real yields on many inflation-linked government stocks are negative. Default edit There is always the risk the borrower will become bankrupt, abscond or otherwise default on the loan. The risk premium attempts to measure the integrity of the borrower, the risk of his enterprise succeeding and the security of any collateral pledged. For example, loans to developing countries have higher risk premiums than those to the us government due to the difference in creditworthiness. An operating line of credit to a business will have a higher rate than a mortgage loan. The creditworthiness of businesses is measured by bond rating services and individual's credit scores by credit bureaus. The risks of an individual debt may have a large standard deviation of possibilities.

The return they might obtain from competing investments is a factor in determining the interest rate they demand. Inflation edit since the lender is deferring shortage consumption, they will wish, as a bare minimum, to recover enough to pay the increased cost of goods due to inflation. Because future inflation is unknown, there are three ways this might be achieved: Charge x interest "plus inflation" Many governments issue "real-return" or "inflation indexed" bonds. The principal amount or the interest payments are continually increased by the rate of inflation. See the discussion at real interest rate. Decide on the "expected" inflation rate. This still leaves the lender exposed to the risk of "unexpected" inflation.

The rule provides a good indication for interest rates up. In the case of juan an interest rate of 18 percent, the rule of 72 predicts that money will double after 72/18 4 years. P.)displaystyle.1841.9388text (4. P.) In the case of an interest rate of 24 percent, the rule predicts that money will double after 72/24 3 years. P.)displaystyle.2431.9066text (4. P.) Market interest rates edit There are markets for investments (which include the money market, bond market, as well as retail financial institutions like banks) set interest rates. Each specific debt takes into account the following factors in determining its interest rate: Opportunity cost and deferred consumption edit Opportunity cost encompasses any other use to which the money could be put, including lending to others, inventory investing elsewhere, holding cash, or spending the funds. Charging interest equal to inflation preserves the lender's purchasing power, but does not compensate for the time value of money in real terms. The lender may prefer to invest in another product rather than consume.

Payments remain constant over the life of the loan; however, payments are allocated to interest in progressively smaller amounts. In a one-year loan, in the first month, 12/78 of all interest owed over the life of the loan is due; in the second month, 11/78; progressing to the twelfth month where only 1/78 of all interest is due. The practical effect of the rule of 78s is to make early pay-offs of term loans more expensive. For a one-year loan, approximately 3/4 of all interest due is collected by the sixth month, and pay-off of the principal then will cause the effective interest rate to be much higher than the apy used to calculate the payments. 12 In 1992, the United States outlawed the use of "Rule of 78s" interest in connection with mortgage refinancing and other consumer loans over five years in term. 13 Certain other jurisdictions have outlawed application of the rule of 78s in certain types of loans, particularly consumer loans. 12 Rule of 72 edit main article: Rule of 72 to approximate how long it takes for money to double at a given interest rate,. E., for accumulated compound interest to reach or exceed the initial deposit, divide 72 by the percentage interest rate. For example, compounding at an annual interest rate of 6 percent, it will take 72/6 12 years for the money to double.

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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 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: rBmn displaystyle frac rcdot Bcdot mnfrac 6times 10,000times 12300 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. In total, the investor therefore now holds: 10,000300left(1frac rnright)cdot Bleft(1frac 62right)times 10,000 and so earns a coupon at the end of the next 6 months of: beginalignedfrac rcdot Bcdot mn frac 6times left(10,000300right)2 frac 6times left(1frac 62right)times 10,0002 309endaligned Assuming the bond remains priced. Their interest is calculated as (100 p p where p is the price paid. Instead of normalizing it to a year, the interest is prorated by the number of days t : (365/ t )100.

(see also: day count convention ). The total calculation is (100 p p 365/ t )100). This is equivalent to calculating the price by a process called discounting at a simple interest rate. Rule of 78s edit main article: Rule of 78s In the age before electronic computing power was widely available, flat rate consumer loans in the United States of America biology would be priced using the rule of 78s, or "sum of digits" method. (The sum of the integers from 1 to 12.) The technique required only a simple calculation.

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. 11 In 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. Calculation of interest edit simple interest edit simple interest 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,. Simple interest is calculated according to the following formula: rBmndisplaystyle frac rcdot Bcdot mn where r is the simple annual interest rate b is the initial balance m is the number of time periods elapsed and n is the frequency of applying interest. For example, imagine that a credit card holder has an outstanding balance of 2500 and that the simple annual interest rate.99 per annum, applied monthly, so the frequency of applying interest is 12 per year. Over one month,.06displaystyle frac.1299times 25001227.06 interest is due (rounded to the nearest cent). Simple interest applied over 3 months would.19displaystyle frac.1299times 2500times 31281.19 If the card holder pays off only interest at the end of each of the 3 months, the total amount of interest paid would.06 per month3 months81.18displaystyle frac.1299times 250012times 327.06text per. (The one cent difference arises due to rounding to the nearest cent.) Compound interest edit main article: Compound interest see also: rate of return Compound interest includes interest earned on the interest which was previously accumulated. Compare for example a bond paying 6 percent biannually (i.e., coupons of 3 percent twice a year) with a certificate of deposit ( gic ) which 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 biannual bond receives half the 6 per year after only 6 months ( time preference and so has the opportunity to reinvest the first 3 coupon payment.

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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 the benefit to the borrower, and interest received by the lender in terms of a premium for the risk of default. Citation needed In the sixteenth century, martín de azpilcueta working 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 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,.

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. Citation needed Islamic finance edit main article: Islamic banking going and finance The latter half of the 20th century saw 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. Citation needed 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 is prohibited, as well as making money out of money is unacceptable. All financial transactions must be asset-backed and it does not charge any interest or fee for the service of lending. Economics edit In economics, the rate of interest is the price of credit, and it plays the role of the cost of capital.

8 9 Catholic Church opposition to interest hardened in the era of scholastics, when even defending it was considered a heresy. 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 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. Citation needed 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. 10 For 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 the appearance of appropriate conditions for entrepreneurs to start new, lucrative businesses.

the rate of interest 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 essay 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. 4 In practice, interest is most often calculated on a daily, monthly, or yearly basis, and its impact is influenced greatly by its compounding rate. Contents History edit According to historian paul Johnson, the lending of "food money" was commonplace in Middle eastern civilizations as early as 5000. The argument that acquired seeds and animals could reproduce themselves was used to justify interest, but ancient Jewish religious prohibitions against usury ( nesheKh ) represented a "different view". 5 While the traditional Middle eastern views on interest was the result of the urbanized, economically developed character of the societies that produced them, the new Jewish prohibition on interest showed a pastoral, tribal influence. 6 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.

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For other uses, see, interest (disambiguation). A bank sign in Malawi advertises the interest rates for lending money to its customers. Interest is story payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (i.e., the amount borrowed at a particular rate. 1, 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. 2 3, 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. In 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.

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