Russian
Cash card, Russian Card for receiving cash from the machine.
Money supply, Russian The total money supply that determines the national economy and is in circulation.
Monetary system, Russian
Russian Assets and liabilities that are expressed in a fixed monetary value, for example: balance bank account, trade debtors, loans and trade creditors.
Money and clothing lottery, Russian , see lottery.
Monetary policy, Russian The set of measures in the field of money circulation and credit aimed at regulating economic growth, curbing inflation, providing employment and equalizing the balance of payments; serves as one of the most important methods of state intervention in the process of reproduction.
Monetary regulation, Russian One of the main means of state influence on economic processes. d.-k.r. economy of the Russian Federation is carried out by the Bank of Russia. he defines the rules required reserves, discount rates for loans, establishes economic standards for commercial banks, conducts transactions with securities. The Bank of Russia, in cooperation with the Government of the Russian Federation, develops and implements a unified state monetary policy aimed at protecting and ensuring the stability of the ruble.
Cash reward, Russian Reward in cash.
Money disaggio, Russian Exchange rate deviation valuable papers, stock values or banknotes downward in comparison with their face value. disaggio is usually expressed as a percentage of the face value.
Monetary allowance, Russian View material support military personnel established by the state. d.d. regulated by the federal law of the Russian Federation of May 27, 1998 No. 76-fz "on the status of military personnel" and others regulations. the circle of persons entitled to d.d. composition d.d. consists
Money measurement, Russian End-to-end measurement of results business transactions with the help of money, providing comparable results.
Cash security, Russian
Cash security, Russian A form of collateral for a loan that consists of maintaining a reserve fund from which payments can be made in case of losses and the presentation of relevant claims by investors.
Money circulation, Russian
Monetary obligation, Russian The obligation of one party to pay money to the other party on the basis of an agreement, as a result of causing harm and for other reasons. see also order of repayment of claims under the monetary obligation.
Cash cover, Russian The firm's degree of availability financial support required to make all payments on time.
Cash allowance, Russian
- cash benefits
Directly, Russian Directly, directly, first hand. arch. from the second (fifth, tenth) hands. , myself
Interest rate(interest rate) - the amount indicated as a percentage of the loan amount, which the recipient of the loan pays for using it for a certain period (month, quarter, year).
From the position of the theory of money, the interest rate is the price of money as.
Interest income is income from the provision of capital in debt in various forms ( , ), or it is income from investments in .
Interest rate is a fixed rate at which deadlines interest is paid. Typically, the interest rate characterizes the ratio annual amount percent ( interest income) to the principal amount. The interest rate is also used in the process of accruing value.
Interest rate is a fee charged by banks for loans. The interest rate is the basis of the cost accounting of banks. The interest rate depends on the size of the loan, its maturity, on the ratio of supply and demand for, as well as the degree of risk that a credit institution bears when lending a certain amount debtor.
History of interest rates
In the last two centuries, basic interest rates set either by national governments or central banks. For example, the Federal Reserve Rate on federal funds The US ranged from 0.25% to 19% between 1954 and 2008, while base rates ranged from 0.5% to 15% between 1989 and 2009, and the spread base rates in Germany was from close to 90% in the 1920s to around 2% in the 2000s. During an attempt to reverse the hyperinflationary spiral in 2007, the Reserve Bank of Zimbabwe raised interest rates on loans to 800%.
Central bank interest rates
Interest rate - the rate of the central bank on operations with other credit institutions. Through the central bank, it has the ability to influence the interest rates of commercial banks, in the country and.
When interest rates decrease, business activity rises and inflation rises. An increase in interest rates leads to a decrease business activity, reducing inflation and appreciation of the national currency.
The main interest rate in the United States: the Federal funds rate - the interest rate at which banks place available funds, located on accounts in the United States, to other banks on .
The rate in the Eurozone is the Refinancing tender rate - the interest rate that is the lowest possible for applications to raise funds in a tender.
Japan's main interest rate: The target interest rate on overnight loans is the level of interest that it wants to see as an average in the market for short-term deposits.
The interest rate, which is the main one in the UK, the so-called interest rate (Repo rate) is the rate at which the Bank of England issues short-term loans secured by securities.
The base rate for Canada: the target overnight rate (Overnight rate target) is the level of interest that the Bank of Canada wants to see as an average in the market for short-term deposits. To control the level of interest rates in the overnight market, the Bank of Canada establishes a so-called operating range with a width of 0.50%, the middle of which is always the target overnight interest rate.
Australia: interest rate Australian dollar overnight (Cash rate) - an interest rate determined as a result of supply and demand in the money market. Reserve Bank Australia sets the required level of this rate and maintains it by controlling .
Interest rates
Interest rates on loans can be greater than zero, equal to zero (" interest-free loan”) and less than zero (“negative” percentages). If interest rates reach a high value, this leads to usury.
Types of interest rates
There are several types of interest rates.
Fixed and floating rates
Depending on whether the rate changes over time, there are fixed and floating interest rates:
- - permanent, set to certain period and does not depend on any circumstances.
- subject to periodic review. The change in the rate is carried out on the basis of fluctuations of certain indicators. A classic example such indicators is (LIBOR, weighted average rate in London interbank market credit resources). Accordingly, the floating rate LIBOR + 5% will mean that the nominal value of the interest rate is 5% higher than the LIBOR rate.
Decursive and antisipative rates
Depending on the timing of interest payments, there are two types of interest rates:
- decursive rate- interest is paid at the end together with the principal amount of the loan;
- antisipative rate- the interest is paid at the time of the loan (in advance) and is determined on the basis of the final amount of the debt.
For the lender, the antisipative rate is more profitable, and for the borrower, the decursive rate. So, if the interest rate is 10%, then at a decursive rate on a loan of $1,000, the lender will receive $1,100 at the end of the term. At the antisipative rate, he will give the borrower $900 and at the end of the term he will receive $1000.
Real and nominal rates
Distinguish between nominal and real interest rates.
Real interest rate is the interest rate taking into account .
The relationship between the real, nominal rate and inflation is generally described by the following (approximate) formula:
I r = I n - I iwhere I r- real interest rate;
I n- nominal interest rate;
I i- the expected or planned level of inflation.
Irving Fisher proposed a more precise formula for the relationship between real, nominal rates and inflation, expressed by the Fisher formula named after him:
I r = (1 + I n)/(1 + I i) - 1 = (I n - I i)/(1 + I i)At I i = 0 and I i = I n both formulas give the same value. It is easy to see that for small values of the inflation rate I i the results differ little, but if inflation is high, then Fisher's formula should be applied.
According to Fisher, the real interest rate must be numerically equal to the marginal productivity of capital.
Surely everyone who has ever taken a loan or become a bank depositor, first came across the concept of "bank interest rate":
The interest rate is the amount, expressed as a percentage, which is set by the bank for the use of a loan and paid for a certain period - a year, a quarter or a month.
- If the money is deposited in a current bank account or deposit, the depositor is the bank's creditor and the bank itself is the borrower.
- If the client borrows money from the bank (takes a loan), then the bank is now the lender, and the client is the borrower.
Knowing these simple truths will save you from the complexes that banks inspire in the population, explaining to them many kilometers of formulas for calculating interest with Newton's binomials, factorials, complex roots, powers and other mathematical crap complexity.
The interest rate determines the price of money
In either of these two cases, the interest rate has a valuing monetary dimension: what will be the savings of the depositor or the bank in a month, a year or several years.
The interest rate on depositors' deposits is usually lower than the rate on bank loans. This is the main income of banking and financial institutions- to take money at a lower price and dispose of it by re-borrowing at a higher one.
For depositors, a deposit is mainly a way to save money, not earn money, so deposit rates are now low, and in some European banks they are even negative.
The base interest rate is the lowest credit interest provided to large trusted campaigns and clients. The BPS is usually set by central banks.
Historical note on rates
The historical range of rates is impressive:
- In Germany, for example, the base interest rate fluctuated between 90% and 2% between 1920 and 2000.
- In the UK - 0.5 - 15% in 1989 - 2009.
- In the US, the US Federal Reserve rate in 1954 - 2008 varied between 19% and 0.25%.
- In Zimbabwe, during the hyperinflationary period of 2007, the lending rate reached 800%.
Types of bets
Fixed and floating rates
Interest rates are:
- Fixed - unchanged for a certain period of time.
- Floating - changeable and periodically reviewed by the bank, depending on some indicators.
So, the classic indicator is LIBOR - average rate London Interbank Credit Exchange.
Many banks determine the floating rate by the formula: LIBOR + n, where n is the fixed rate of a particular bank.
Russian banks can rely on an independent indicative rate, such as the MosPrime Rate.
In the growing market of loan rates, it is more profitable for a borrower to take a loan at a fixed interest rate.
By the time of payment, bets are:
- decursive - paid at the end along with the repayment of the loan;
- antisipative - paid in advance when granting a loan.
Decursive rates are beneficial for borrowers, and antisipative rates are beneficial for lenders, but banks usually act in their own interests:
- interest on deposits is calculated decursively,
- credit - antisipative: when issuing a loan, the total interest is immediately determined, which is then divided by the number of periods (usually months).
decursive and antisipative ways are used in calculating simple and compound interest, when the initial amount of capital changes in each reporting period.
- The decursive method is convenient to use with floating rates.
- The antisipative method is convenient during periods of instability as a guarantor of the payment of compound interest.
The decursive rate is also called the loan interest, since it determines the ratio of the income received (interest) to the initial amount of money.
How to calculate the loan interest and the amount of buildup
The formula for determining the loan interest:
i = I/P (1), where:
- i (income) - loan interest;
- I - the sum of all accrued for reporting period percent;
- P - initial monetary amount (present value).
The amount of growth F (future value) is determined by the formula:
F = P + i*n*P = P*(1 + i*n). (2)
Here n is the number of billing periods.
The ratio F/P is the growth factor k n .
k n = 1 + i*n. (3)
Calculation of the amount of extensionF is called compounding.
Compounding on the calculation example
- Let's make compounding bank loan in the amount of 1 million rubles, issued at 12% per annum (simple rate), for a period of 10 years according to formula (2)
F \u003d 1,000,000 * (1 + 0.12 * 10) \u003d 2,200,000 rubles.
The initial amount of money issued by the bank on a long-term ten-year loan, often used in mortgages, increased by 1,200,000 rubles, that is, more than doubled.
- You can also calculate the amount of growth for a short period (less than a year). In this case, the definition formula F (2) is transformed:
F = P * (1 + i * d/K). (four)
- d - quantity calendar days for which the loan was taken;
- K is the number of days in a year, i.e. 365 or 366.
Let us calculate the accrued amount of a loan in the amount of 50,000 rubles issued by an MFO at the annual simple rate of 15% specified in the agreement for a period of 91 days.
Inserting the values into formula (4), we obtain:
F \u003d 50,000 * (1 + 0.15 * 91/365) \u003d 51,870 rubles.
Often, banks and MFIs require the return of amounts greater than the calculated ones - this means that additional hidden interest was calculated in the form of various commissions. Before concluding an agreement, you should carefully read all its clauses in search of illegal ways to increase capital.
Discounting
The reverse operation - the calculation of the initial amount P by the accrued F - is called discounting.
Discounting is calculated according to the formula:
P = F/ (1 + i*n). (5)
Let's calculate according to the formula (5):
P \u003d 100,000 / (1 + 0.1 * 3) \u003d 76,923 rubles.
Floating rate settlements
If the rate is floating, then the accumulated amount is calculated by summing the rates for each period of their change, and the formula is converted into some kind of abstract formula:
F = P *(1 + ∑(1…N) n*i) (6), where:
- n is a period from one to N;
- i - variable rate;
- ∑(1…N) is the sum of products n*i for all calculation periods.
It looks scary at first glance, but how this happens is very easy to understand by the example:
We use formula (6) for calculation:
F = 500,000 *(1 + 0.11 + 0.5 (0.125 + 0.14 + 0.155 + 0.17)) = 500,000 * 1.405 = 702,500 rubles.
Pay attention to the fact that the growth factor k, calculated at a fixed percentage by formula (3), at a floating percentage is determined by the expression in brackets of formula (6):
K = 1 + ∑(1…N) n*i. (7)
AT this example its value is 1.405.
Compound interest calculations
This calculation method is banking is used when accruing interest on long-term deposits, when interest is accrued on the amount accrued by previous interest.
The formula for calculating compound interest is shown in the figure below.
Rate and inflation
The interest rate can be nominal and real:
- Nominal - set by the bank.
- Real - adjusted for inflation.
The real rate i real is less than the nominal rate i nom by the inflation rate π.
i real \u003d i nom - π.
This formula is usually used when inflation is low. With a large inflation level, calculations are made using the more complex Fisher formula:
i real \u003d (i nom - π) / (1 + π).
The real value of money
To determine the real value of money, taking into account inflation over time, use the formula:
R= N/(1+i)ª.
R is the real value of money;
N is the nominal value;
i - inflation rate;
a is the number of periods (years, months, etc.).
Banks usually raise interest credit rate during periods of high inflation, laying its growth in the nominal rate. Such a step, in addition to fighting the fall in the price of money, gives them the opportunity to raise the interest rate on deposits so as not to lose depositors.
Financial illiteracy of the population is beneficial to bankers
Sometimes lending rates, especially fast loans, contradict common sense and are a veiled scam. Therefore, understanding what bank interest and how to calculate the amount of the increase should be for everyone who wants to take a loan.
Taking advantage of the financial illiteracy of the population, banks today offer such intricate and complex calculation formulas that an engineer or programmer's calculator requires. Meanwhile, it is quite simple to calculate the total amount of loan payments (aka the amount of the increase), as can be seen from the examples, on a regular calculator and even on a piece of paper. It can be calculated according to different formulas for payments on the body of the loan and on interest, but the deviations between your final calculations and bank ones should still not be too large. Moreover, here are the formulas for calculating simple rather than compound interest, which does not contradict the principles of annuity payments used today in lending.
Banks today practically do not use a differentiated method of repaying a loan, in which the remaining amount of the debt, and not the initial one, is taken into account when calculating interest. This is allegedly motivated by “concern for customers”: why, they say, should they strain their brains and make complex calculations every month? Thus, it turns out that our lending is one of the most unprofitable in the world.
For a particular currency, the interest rate is the price sums of money in that currency, that is, the cost of borrowing in that currency.
The interest rate is formed in the money market under the influence of supply and demand: the more those who want to borrow money, the higher it is; the more those who are willing to lend money, the lower it is.
State governments through Central Banks control the interest rate in the money markets, limiting the amount of money in circulation. The size of the interest rate affects the economic activity in the country. If the interest rate rises, and therefore loans become more expensive, then projects financed by borrowed money become less attractive because they must be more profitable to cover costs. In other words, high interest rates suppress economic activity and make it impossible to implement a number of projects. On the contrary, a decrease in interest contributes to the growth of economic activity, increasing the attractiveness of projects with debt financing.
Impact of interest rates on the global market
Most business globally is financed by loans of a similar nature. The "value" of these loans is determined by the respective interest rates. The higher the rate, the more profitable the business must have in order to cover the interest on the loan.
Essentially, the interest rate is the cost of doing business that affects every individual. The interest rates that consumers and homeowners pay on their credit cards and mortgage loans originate from money markets.
Interest rates determine what it costs an organization or individual to use borrowed funds over a period of time. certain period time. The expression “time is money” means that as long as the borrower owes money, interest is charged on the principal amount of the loan.
The role of interest rates
Market participants are always looking for ways to increase profits. The key criterion for assessing the prospects of investments is the real rate of return on them. For the currency in which investments are made, this rate is determined in the following way:
Real Rate of Return = Interest Rate - Apparent Inflation Rate
Money flows to countries with the highest real rates of income. Central banks sometimes raise interest rates to attract capital into the country. high stakes attract capital, which allows us to hope for an increase in demand for national currency and for promotion exchange rate. For getting high income market participants must invest capital in the country and buy its national currency.
When the central bank raises interest rates, real rates of return in national economy grow, which attracts capital to the country. On the contrary, a decrease in interest rates entails an outflow of capital from the country. The inflow or outflow of capital strengthens or weakens the currency accordingly. Thus, by changing interest rates in the national money market, central bank affects the exchange rate.
Interest rates money market linked to rates in other sectors financial market, a discount rate Central Bank, the rate on treasury bills, interbank rates on overnight loans ("day money") are the base for the entire system of interest rates.
AT different countries The interest rate of the Central Bank is called differently:
- - discount rate in the USA, in Germany, in Japan and in Switzerland
- - intervention course in France
- - bank rate In Canada
- - UK money market dealing rate
- - refinancing rate in Russia
And the calculation of the parameters of this transaction.
The course of financial mathematics consists of two sections: one-time payments and streams of payments. One-time payments- these are financial transactions in which each party, when implementing the terms of the contract, pays the amount of money only once (either lends or repays the debt). Payment flows- These are financial transactions in which each party, when implementing the terms of the contract, makes at least one payment.
There are two parties involved in a financial transaction: the lender and the borrower. Each party can be both a bank and a client. Main financial transaction- lending a certain amount of money. Money is not equal in relation to time. Modern money is usually more valuable than future money. The time value of money is reflected in the amount of accrued interest money and the scheme of their accrual and payment.
The mathematical apparatus for solving such problems is the concept of "percentage" and and .
Interest - basic concepts
Percent- one hundredth of a predetermined base (that is, the base corresponds to 100%).
Examples:Answer: more
| original amount of debt | |
| (days) | a fixed period of time to which the interest (discount) rate is timed (usually one year - 365, sometimes 360 days) |
| interest (discount) rate for the period | |
| debt term in days | |
| debt term in fractions of the period | |
| the amount due at the end of the term |
Interest rate
Interest rate- the relative amount of income for a fixed period of time. The ratio of income (interest money - the absolute value of income from lending money) to the amount of debt.
Accrual period- this is the time interval for which the interest rate is timed, it should not be confused with the accrual period. Usually I take a year, half a year, a quarter, a month as such a period, but most often they deal with annual rates.
Interest capitalization- adding interest to the principal amount of the debt.
Accretion- the process of increasing the amount of money in time in connection with the addition of interest.
Discounting- inversely accretion, in which the amount of money relating to the future is reduced by the amount corresponding to the discount (discount).
The value is called the accumulation multiplier, and the value is called the discount multiplier with the appropriate schemes.
Interest rate interpretationWith the scheme " simple interest"The initial basis for calculating interest over the entire term of the debt for each period of application of the interest rate is the initial amount of the debt.
With the scheme " compound interest"(for integers) the initial basis for accruing interest over the entire period for each period of application of the interest rate is the accrued for previous period debt amount.
The addition of accrued interest money to the amount that serves as the basis for their calculation is called interest capitalization (or reinvestment of the deposit). When applying the "compound interest" scheme, capitalization of interest occurs on each period.
Discount rate interpretationUnder the "simple interest" scheme ( simple discount) - the initial basis for interest accrual over the entire term of the debt for each period of application of the discount rate is the amount payable at the end of the deposit term.
With the "compound interest" scheme (for integers) ( compound discount) - the initial basis for accruing interest over the entire period for each period of application of the discount rate is the amount of debt at the end of each period.
Simple and compound interest rates
"Direct" formulas
| Simple interest | Compound interest | ||
| - interest rate |  |
 |
buildup |
| - interest rate |
 |
 |
discounting (bank accounting) |
"Reverse" formulas
| Simple interest | Compound interest | ||
| - interest rate | discounting (mathematical accounting) | ||
| - interest rate | buildup |
Variable interest rate and reinvestment of deposits
Let the debt term have stages, the length of which is equal to , ,
- simple interest scheme
1 . The contract provides for the accrual of a) simple, b) compound interest in the following order: in the first half of the year at an annual interest rate of 0.09, then in next year the rate decreased by 0.01, and in the next two half-years it increased by 0.005 in each of them. Find the value of the accrued deposit at the end of the term, if the value of the initial deposit is $800.
Market interest rate as the most important macroeconomic indicator
The interest rate is important. The interest rate is the fee for the money provided in . There were times when the law did not allow remuneration for the fact that unspent, borrowed money was lent. AT modern world widely use loans, for the use of which a percentage is set. Since interest rates measure the costs of using money by entrepreneurs and the reward for not using money by the consumer sector, the level of interest rates plays a significant role in the economy of the country as a whole.
Very often in economic literature use the term "interest rate", although there are many interest rates. Differentiation of interest rates is associated with the risk taken by the lender. The risk increases with the length of the loan, as it becomes more likely that the money may be required by the lender before the due date of the loan, the interest rate increases accordingly. It increases when a little-known entrepreneur applies for a loan. A small firm pays a higher interest rate than a large one. For consumers, interest rates also vary.
However, no matter how different interest rates are, they are all affected: if the money supply decreases, then interest rates increase, and vice versa. That is why the consideration of all interest rates can be reduced to the study of the patterns of one interest rate and in the future to operate with the term "interest rate"
Distinguish between nominal and real interest rates
Real interest rate is determined taking into account the level. It is equal to the nominal interest rate, which is set under the influence of supply and demand, minus the inflation rate:
If, for example, a bank lends and charges 15%, and the inflation rate is 10%, then the real interest rate is 5% (15% - 10%).
Interest calculation methods:
Simple interest rate
simple interest chart
Determine the interest and the amount of accumulated debt if the simple interest rate is 20% per annum, the loan is 700,000 rubles, the term is 4 years.
- I \u003d 700,000 * 4 * 0.2 \u003d 560,000 rubles.
- S \u003d 700,000 + 560,000 \u003d 1,260,000 rubles.
Situation when the term of the loan is less than the accrual period
The time base can be equal to:- 360 days. In this case one gets ordinary or commercial interest.
- 365 or 366 days. Used to calculate exact interest.
- Exact Number of Loan Days - Determined by counting the number of days between the date of the loan and the date of its repayment. The day of issue and the day of redemption are considered as one day. The exact number of days between two dates can be determined from the table of ordinal numbers of days in a year.
- Approximate number of loan days - determined from the condition that any month is taken equal to 30 days.
- Accurate interest with exact number of loan days (365/365)
- Ordinary interest with the exact number of loan days (bank; 365/360). If the number of loan days exceeds 360, this way leads to the fact that the amount of accrued interest will be more than provided for by the annual rate.
- Ordinary interest with an approximate number of loan days (360/360). It is used in intermediate calculations, as it is not very accurate.
A loan in the amount of 1 million rubles was issued on January 20 to October 5 inclusive at 18% per annum. How much must the debtor pay at the end of the term when calculating simple interest? Calculate in three ways to calculate simple interest.
To begin with, let's determine the number of loan days: January 20 is the 20th day of the year, October 5 is the 278th day of the year. 278 - 20 \u003d 258. With an approximate calculation - 255. January 30 - January 20 \u003d 10. 8 months multiplied by 30 days \u003d 240. total: 240 + 10 + 5 \u003d 255.
1. Accurate interest with the exact number of loan days (365/365)
- S \u003d 1,000,000 * (1 + (258/365) * 0.18) \u003d 1,127,233 rubles.
2. Ordinary interest with exact number of loan days (360/365)
- S \u003d 1,000,000 * (1 + (258/360) * 0.18 \u003d 1,129,000 rubles.
3. Ordinary interest with approximate number of loan days (360/360)
- S \u003d 1,000,000 (1 + (255/360) * 0.18 \u003d 1,127,500 rubles.
Variable rates
Loan agreements sometimes provide for time-varying interest rates. If this simple bets, then the accumulated amount at the end of the term is determined as follows.
