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The rate of interest is given by the intersection of the solid red saving curve with the blue investment schedule. But so long as the investment schedule is almost vertical, a change in income leading in extreme cases to the broken red saving curve will make little difference to the interest rate.
In some cases the analysis will be less simple. The introduction of a new technique, leading to demand for new forms of capital, will shift the step to the right and reduce its steepness. In the case of extraordinary spending in time of war the government may wish to borrow more than the public would be willing to lend at a normal interest rate.
If the dotted red curve started negative and showed no tendency to increase with r , then the government would be trying to buy what the public was unwilling to sell at any price. Keynes mentions this possibility as a point "which might, perhaps, have warned the classical school that something was wrong" p. He also remarks on the same page that the classical theory doesn't explain the usual supposition that "an increase in the quantity of money has a tendency to reduce the rate of interest, at any rate in the first instance".
Keynes's diagram of the investment schecule lacks the step shape which can be seen as part of the classical theory. He objects that. Later p. The classical theory of interest explains it as the capitalist's share of business profits, but the pre-marginalist authors were unable to reconcile these profits with the labor theory of value excluding Longfield, who was essentially a marginalist. Their responses often had a moral tone: Ricardo and Marx viewed profits as exploitation, and McCulloch 's productivity theory justified profits by portraying capital equipment as an embodiment of accumulated labor.
Knut Wicksell published his "Interest and Prices" in , elaborating a comprehensive theory of economic crises based upon a distinction between natural and nominal interest rates. Wicksell's contribution, in fact, was twofold.
First he separated the monetary rate of interest from the hypothetical "natural" rate that would have resulted from equilibrium of capital supply and demand in a barter economy, and he assumed that as a result of the presence of money alone, the effective market rate could fail to correspond to this ideal rate in actuality.
Next he supposed that through the mechanism of credit, the rate of interest had an influence on prices; that a rise of the monetary rate above the "natural" level produced a fall, and a decline below that level a rise, in prices. But Wicksell went on to conclude that if the natural rate coincided with the monetary rate, stability of prices would follow.
In the s Wicksell's approach was refined by Bertil Ohlin and Dennis Robertson and became known as the loanable funds theory. The doyen of the Austrian school, Murray N. Rothbard, sees the emphasis on the loan market which makes up the general analysis on interest as a mistaken view to take. As he explains in his primary economic work, Man, Economy, and State , the market rate of interest is but a manifestation of the natural phenomenon of time preference, which is to prefer present goods to future goods.
Too many writers consider the rate of interest as only the price of loans on the loan market. In reality Interest is explainable by the rate of time preference among the people. To point to the loan market is insufficient at best. Rather, the rate of interest is what would be observed between the "stages of production", indeed a time market itself, where capital goods which are used to make consumers' goods are ordered out further in time away from the final consumers' goods stage of the economy where consumption takes place.
It is this spread between these various stages which will tend toward uniformity , with consumers' goods representing present goods and producers' goods representing future goods, that the real rate of interest is observed. Rothbard has said that.
Interest rate is equal to the rate of price spread in the various stages. Rothbard has furthermore criticized the Keynesian conception of interest, saying. One grave and fundamental Keynesian error is to persist in regarding the interest rate as a contract rate on loans, instead of the price spreads between stages of production.
The interest rate, being one of the many elements of the general system of equilibrium, was, of course, simultaneously determined with all of them so that there was no point at all in looking for any particular element that 'caused' interest. Interest is one of the main components of the economic theories developed in Keynes 's General theory of employment, interest, and money.
In his initial account of liquidity preference the demand for money in Chapter 13, this demand is solely a function of the interest rate; and since the supply is given and equilibrium is assumed, the interest rate is determined by the money supply. In his later account Chapter 15 , interest cannot be separated from other economic variables and needs to be analysed together with them. See The General Theory for details. Jews are forbidden from usury in dealing with fellow Jews, and this lending is to be considered tzedakah , or charity.
However, there are permissions to charge interest on loans to non-Jews. From the Jewish Publication Society 's Tanakh,  with Christian verse numbers, where different, in parentheses:. 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. Thou shalt not lend upon interest to thy brother: interest of money, interest of victuals, interest of any thing that is lent upon interest. Unto a foreigner thou mayest lend upon interest; but unto thy brother thou shalt not lend upon interest; that the LORD thy God may bless thee in all that thou puttest thy hand unto, in the land whither thou goest in to possess it.
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. Several historical rulings in Jewish law have mitigated the allowances for usury toward non-Jews. For instance, the 15th-century commentator Rabbi Isaac Abrabanel 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 Kimchi extended this principle to non-Jews who show consideration for Jews, saying they should be treated with the same consideration when they borrow. The following quotations are English translations from the Qur'an :. Those who charge usury are in the same position as those controlled by the devil's influence.
This is because they claim that usury is the same as commerce. However, God permits commerce, and prohibits usury. Thus, whoever heeds this commandment from his Lord, and refrains from usury, he may keep his past earnings, and his judgment rests with God. As for those who persist in usury, they incur Hell, wherein they abide forever. God condemns usury, and blesses charities. God dislikes every sinning disbeliever.
Those who believe and do good works and establish worship and pay the poor-due, their reward is with their Lord and there shall no fear come upon them neither shall they grieve. O you who believe, you shall observe God and refrain from all kinds of usury, if you are believers. If you do not, then expect a war from God and His messenger. But if you repent, you may keep your capitals, without inflicting injustice, or incurring injustice.
If the debtor is unable to pay, wait for a better time. If you give up the loan as a charity, it would be better for you, if you only knew. O you who believe, you shall not take usury, compounded over and over. Observe God, that you may succeed.
And for practicing usury, which was forbidden, and for consuming the people's money illicitly. We have prepared for the disbelievers among them painful retribution. The usury that is practiced to increase some people's wealth, does not gain anything at God. But if people give to charity, seeking God's pleasure, these are the ones who receive their reward many fold. O People, just as you regard this month, this day, this city as Sacred, so regard the life and property of every Muslim as a sacred trust.
Return the goods entrusted to you to their rightful owners. Hurt no one so that no one may hurt you. ALLAH has forbidden you to take usury, therefore all usurious obligation shall henceforth be waived. Your capital, however, is yours to keep. You will neither inflict nor suffer any inequity. Allah has Judged that there shall be no usury and that all the usury due to Abbas ibn 'Abd'al Muttalib Prophet's uncle shall henceforth be waived The Old Testament "condemns the practice of charging interest 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 is exploiting that person and dishonoring God's covenant Exodus —27 ".
The first of the scholastic Christian theologians, Saint Anselm of Canterbury , led the shift in thought that labeled charging interest the same as theft. Previously usury had been seen as a lack of charity. Thomas Aquinas , the leading scholastic theologian of the Roman 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. 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 that anyone can charge. In condemning usury Aquinas 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 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 is usury.
St Thomas quotes Aristotle as saying that "to live by usury is exceedingly unnatural". Islam likewise condemns usury but allowed commerce Al-Baqarah — an alternative that suggests investment and sharing of profit and loss instead of sharing only profit through interests. Judaism condemns usury towards Jews, but allows it towards non-Jews Deut. 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, for example, 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 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. This idea is very similar to opportunity cost.
Many scholastic thinkers who argued for a ban on interest charges also argued for the legitimacy of lucrum cessans profits for example, Pierre Jean Olivi and St. Bernardino of Siena. However, Hostiensis' exceptions, including for lucrum cessans , were never accepted as official by the Roman Catholic Church. The Westminster Confession of Faith , a confession of faith upheld by the Reformed Churches , teaches that usury--charging interest at any rate--is a sin prohibited by the eighth commandment.
The Roman Catholic Church has always condemned usury, but in modern times, with the rise of capitalism and the disestablishment of the Catholic Church in majority Catholic countries, this prohibition on usury has not been enforced. The nature of the sin called usury has its proper place and origin in a loan contract The sin rests on the fact that sometimes the creditor desires more than he has given One cannot condone the sin of usury by arguing that the gain is not great or excessive, but rather moderate or small; neither can it be condoned by arguing that the borrower is rich; nor even by arguing that the money borrowed is not left idle, but is spent usefully It might initially seem like little is at stake when it comes to interest, but this is an issue of human dignity.
A person is made in God's own image and therefore may never be treated as a thing. Interest can diminish the human person to a thing to be manipulated for money. Charging interest is indeed sinful when doing so takes advantage of a person in need as well as when it means investing in corporations involved in the harming of God's creatures. From Wikipedia, the free encyclopedia. This is the latest accepted revision , reviewed on 17 November For other uses, see Interest disambiguation.
A sum paid for the use of money. Main article: Islamic banking and finance. Main article: Interest rate. Main article: Compound interest. See also: rate of return. Main article: Rule of 78s. Main article: Rule of This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed.
January Learn how and when to remove this template message. See also: Fisher equation. Main article: Loans and interest in Judaism. Main articles: Riba and Islamic banking and finance. The tract seems indeed to have been forgotten very soon. Thus, Barbon's fundamental idea remained in abeyance until , when it was again expounded—for all we know, independently rediscovered—by Massie,  whose analysis not only went further than Barbon's but also gathered force from its criticism of the views of Petty and Locke.
Page numbers refer to the widely available edition published by Macmillan for the Royal Economic Society as part of Keynes's collected writings, which appear to correspond to those of the first edition. Fisher also referred to it as representing the "investment opportunity side of interest theory".
Constructs such as ibid. Please improve this article by replacing them with named references quick guide , or an abbreviated title. May Learn how and when to remove this template message. English Oxford Living Dictionaries. Oxford University Press.
Retrieved 27 December Money paid regularly at a particular rate for the use of money lent, or for delaying the repayment of a debt. Merriam Webster. Economics Online. MacTutor History of Mathematics. Retrieved 26 August BBC World Service.
Business Insider. Wipf and Stock Publishers. Retrieved The Christianization of Interest. Church History, 3, p 6. Archived from the original on PBS NewsHour. Auburn, Alabama : Mises Institute. Retrieved 12 March Retrieved 4 January Jewish Virtual Library.
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Traditional amortized loans use the same formulas as those defined above for savings, except that the loan amount is represented as a negative value for the starting principal, P. Payment amounts A are still positive values. The formula for the payment amount is found by solving for A using the formula from Figure 1.
In Excel, you can use the PMT function. Argument 1 : Yes. The table in Example 5 clearly shows that the new principal is calculated by adding the interest and the payment to the previous principal. The formulas are exactly the same as the savings example, except that you are starting with a negative principal. The formulas show that interest IS added to the principal, which satisfies the definition of compound interest, and that explains why you can use the compound interest formulas in traditional loan calculations.
Argument 2 : No. Instead, you must first pay the amount of interest that you are charged, and the rest of your payment is applied to the principal. This is how almost all amortized loans are worded. You are paying the interest first, so no interest is added to the principal.
Therefore, you are not paying interest on interest if your payments are enough to completely pay the interest charged each period. I was in the camp of Argument 2 for many years, and it wasn't until creating these compound interest calculators that I realized Argument 2 is just legal jargon - a way to claim you aren't paying interest on interest.
The parentheses tell us to first add the interest a negative value in this case to the loan payment. Then, the result is added to the principal. Does that actually change the final value? Of course not. Argument 2 then says "Yeah, but your payment is enough to completely pay the amount of interest charged, so no interest is actually added to the principal. Therefore, you aren't paying interest on interest. Argument 1 replies with "Yeah, but without affecting the result, the math allows me to consider my payment to be applied to the original principal, with the interest added afterward.
Thus, I AM paying interest on interest. Argument 2 would then say "Our definition of the loan payment means that you are forced to add the amounts in parentheses first, so we are allowed to say we aren't adding interest to the principal. Which argument is correct? Or, could they both be correct? Ultimately, the fact is that the compound interest formulas calculate the same result for Example 5, regardless.
Ultimately, the take away is that part of your regular loan payment is being used to pay off interest. To take advantage of the compound interest formula, the borrower should make additional principal-only payments. Learn how debt payoff is similar to an investment. Note Even a so-called Simple Interest Loan requires the payments to be applied first to the accrued interest before they can be applied to the principal. So, even though the daily interest accrual is based on simple interest, the amortization is still based on the compound interest formula.
Compound Interest Calculator. See caution below. Compound Interest Calculator for Excel. Fig 1: Formula relating pv, rate, nper, pmt, fv in Excel. References  Compound Interest at wikipedia. Disclaimer : This information on this page is for educational purposes only. We do not guarantee the results or the applicability to your unique financial situation. Have you ever wished for the safety of bonds, but the return potential If you are reaching retirement age, there is a good chance that you Please help us personalize your experience.
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