The upper limit of the interest on the loan is determined by market conditions. The lower limit is calculated taking into account the bank's costs of raising funds and ensuring the functioning of a credit institution. The upper limit of interest on a loan is determined

When calculating the rate of interest in each specific transaction commercial Bank takes into account:

n level of basic interest rate, which is calculated on the basis of the real price of raising funds, the level of other expenses of the bank and the planned rate of profitability of ship operations;

n premium for risk taking into account the conditions loan agreement;

Base interest rates are the average interest rates at which loans are made to first-class borrowers.

The risk premium is differentiated depending on the following criteria:

n creditworthiness of the borrower;

n availability of collateral for the loan;

n loan term;

n the strength of the relationship between the client and the bank;

Considering that the interest on active operations of the bank plays an important role in the formation of income, and the payment for attracted resources occupies a significant place in the composition of its expenses, the problem of determining the interest margin (M fact) is of current importance, i.e. the difference between the average rates on active operations (loans) (Pa) and passive operations of the bank (attracting deposits) (PP):

M fact = Pa - Pp.

The main factors affecting the size of the interest margin are the volume and composition of credit investments and their sources, the timing of payments, the nature of the applied interest rates and their movement.

Depending on the nature of the movement, interest rates can be fixed and floating. The fixed interest rate is established for the entire loan period and is not subject to revision. This is beneficial for both the lender and the borrower, since both parties have the opportunity to accurately calculate their income and expenses associated with the use of the loan provided. Fixed interest rates are usually applied for short-term lending.

A floating interest rate is a rate that constantly changes depending on the situation in the credit markets and the financial market of the country. In world practice, the following groups of floating interest rates are used:

A. Official interest rates (discount rate and refinancing rate) are set by the Central Bank of the country. At these rates, the Central Bank provides loans to commercial banks.

B. Interbank rates of supply of credit resources. Interest rates at which banks provide loans to each other. The most widely used base rate is LIBOR, the London Interbank Offered Rate. These are the rates for deposits in pounds sterling and US dollars. Calculated as the arithmetic average of the fixed rates at 11 am each business day, respectively, 7 banks in England or 5 banks in the United States. The LIBOR rate on Eurocredits is calculated, as a rule, for 12 currencies and for several periods (1 week, 1, 2, 3, 6, 9, 12 months). At the LIBOR rate, lending is carried out between first-class banks in the Eurocurrency market.

C. Prime rate (first-class) rate is the published rate for loans to premium borrowers. It serves as a guideline for the cost of the loan and is usually 1 - 2% higher than the first two rates.

D. The rate of loans to medium and small firms and individuals.

The amount of the loan fee depends on the size of the penalty interest rate. With all the variety of conditions and methods of applying penalty rates, there are certain patterns in them. Their general purpose is to make violation of contractual obligations unprofitable.

Depending on the initial base, the amounts for calculating interest distinguish between simple and compound interest.

Simple interest assumes that the rate is applied to the same initial amount throughout the life of the loan. Compound interest is calculated in relation to the amount with the interest accrued in the previous period.

The amount of interest accrued for the entire period is calculated according to the formula:

I = P * n * i, where

I - the amount of interest for the entire period of use of the loan;

P is the initial amount of the debt;

i is the interest rate determined by the commercial bank;

n - loan term, usually measured in years, and

t is the number of days of the loan;

K - the number of days in a year, which is fixed in the loan agreement. It can be equal to 360 days, then the interest is called ordinary or commercial, or 365,366 days - exact interest. The day of issue and the day of repayment of the loan is considered one day.

The amount of debt for the entire period of use of the loan is determined by the formula:

S = P + I = P (1 + ni), where

S - the amount at the end of the term of the loan.

Compound interest. In long-term financial transactions, when interest is not paid immediately after accrual, but is attached to the principal amount of the debt, compound interest rates are applied for accrual. The base for compound interest increases with each step in time.

The magnitude of the build-up factor depends on the parameters i, n is the number of periods. With a long term increase, even a small change in the rate noticeably affects the value of the multiplier. In turn, a very long term leads to frightening results even at a low interest rate.

Interest is calculated in the amounts and terms stipulated by the agreement, but at least once a quarter and is paid in installments according to the schedule of payment (repayment) of the due interest amounts established by the bank. According to the "Provisions on the procedure for calculating interest and reflecting them on accounts accounting in the institutions of the banks of the State Bank of the USSR dated January 22, 1991, No. 338 with amendments and additions, the accrual and payment of interest in advance at the time of the loan is not allowed. Lump-sum payment of interest on repayment of the principal amount of the debt is allowed only when a loan is issued for a period of not more than 3 months ...

If the amount contributed by the borrower is insufficient to pay off the urgent payment, overdue debt and accrued interest, then interest is paid first, then overdue debt, and the remaining amount is used to repay the principal amount of the share. This procedure is negotiated when concluding a contract.

The main factors that a commercial bank takes into account when setting a loan payment:

Refinancing rate - the official rate of interest on centralized credit resources, which the Central Bank of the Russian Federation provides to commercial banks; (operated from 1992 to 1.01.95) from 1.01.95 the Central Bank stopped providing new centralized loans and switched to refinancing commercial banks only through credit auctions)

Average interest rate on interbank loans;

The average interest rate paid by the bank to its customers on deposits various types;

The structure of the bank's credit resources (the higher the share of borrowed funds, the more expensive the loan).

In conditions market economy where inflation is obligatory, there is a nominal and real interest rate for a loan.

The real rate is adjusted to reflect the growth rate of inflation.

It is the real interest rate that is important when deciding on the use of a loan.

The upper limit of the interest on the loan is determined by market conditions. The lower limit is calculated taking into account the costs of the bank to raise funds and ensure its own functioning.

When calculating the rate of interest in each specific transaction, a commercial bank takes into account:

  • a) the level of the base interest rate, which is calculated on the basis of the real price of raising funds;
  • b) the level of the bank's own expenses;
  • c) the planned rate of profitability of lending operations;
  • d) risk premium, taking into account the terms of the loan agreement.

Base interest rates are the average interest rates at which loans are made to first-class borrowers.

The risk premium is set depending on the following criteria:

  • a) the creditworthiness of the borrower;
  • b) availability of collateral for the loan;
  • c) loan term;
  • d) the relationship of the client with the bank;

Taking into account that the payment for attracted resources occupies a significant place in the composition of the bank's expenses, the issue of the difference between the average rates on loans issued and attracting deposits (interest margin) is of great importance.

Fixed and floating rate.

Interest rates can be fixed and floating.

The fixed interest rate is established for the entire loan period and is not subject to revision. This is beneficial for both the lender and the borrower, since both parties have the opportunity to accurately calculate their income and expenses associated with the use of the loan provided. Fixed interest rates are usually applied for short-term lending.

A floating interest rate is a rate that constantly changes depending on the situation in the credit markets and the financial market of the country.

In world practice, the following groups of floating interest rates are used:

  • 1) Official interest rates (discount rate and refinancing rate) are set by the Central Bank of the country. At these rates, the Central Bank provides loans to commercial banks.
  • 2) Interbank rates of supply of credit resources. Interest rates at which banks provide loans to each other. The most widely used base rate is LIBOR, the London Interbank Offered Rate. These are the rates for deposits in pounds sterling and US dollars. Calculated as the arithmetic average of the fixed rates at 11 am each business day, respectively, 7 banks in England or 5 banks in the United States. The LIBOR rate on Eurocredits is calculated, as a rule, for 12 currencies and for several periods (1 week, 1, 2, 3, 6, 9, 12 months). At the LIBOR rate, lending is carried out between first-class banks in the Eurocurrency market.
  • 3) Prime rate is the published rate for loans to prime borrowers. It serves as a guideline for the cost of the loan and is usually 1 - 2% higher than the first two rates.
  • 4) The rate of loans to small firms and individuals.

Depending on the initial base, the amounts for calculating interest distinguish between simple and compound interest.

Simple interest imply the application of the rate to the same initial amount throughout the entire term of the loan.

Compound interest is calculated in relation to the amount with the interest accrued in the previous period.

Interest is calculated in the amounts and terms stipulated by the agreement, but at least once a quarter, and is paid in installments according to the schedule of repayment of the due interest amounts established by the bank. A lump sum payment of interest upon repayment of the principal amount of a debt is permitted only when a loan is issued for a period not exceeding 3 months. If the amount contributed by the borrower is insufficient to pay off the urgent payment, overdue debt and accrued interest, then interest is paid first, then overdue debt, and the remaining amount is used to repay the principal amount of the share. This procedure is negotiated when concluding a contract.

What determines the interest rate.

The main factors that a commercial bank takes into account when setting a loan payment:

  • - the average interest rate on interbank loans;
  • - average interest rate. paid by the bank to its customers on deposits of various types;
  • - the structure of the bank's credit resources (the higher the share of borrowed funds, the more expensive the loan);
  • - supply and demand for loans from customers. Increased demand leads to higher interest rates;
  • - the term and types of the loan, more precisely the degree of risk for the bank of non-repayment of the loan, depending on the collateral;
  • - stability money circulation in the country (the higher the inflation rate, the more expensive the date for the loan);
  • - the nature of the relationship between the lender and the borrower;
  • - expenses for registration and control over the use and repayment of the loan.

The Central Bank's refinancing rate serves as the main benchmark for the level of loan interest.

The change in the refinancing rate affects the level of lending interest, because interest on the loan is included in the cost of production within the refinancing rate, and in excess of this amount is paid from the profit. Interest on interbank loans is also charged to the bank's expenses only within the limits of the refinancing rate; in excess of this rate, they are charged from the profit.

The lending rate is influenced by the degree of risk of credit investments: the greater the risk, the higher the interest rate. On the other hand, the borrower also has to take risks. If the loan is issued on high rates, the risk of ongoing operations increases significantly, since the borrower needs to invest like this cash to return not only the principal amount of the debt, but also the interest.

  • Chapter 3. The role of money in the reproduction process. Features of its manifestation in different models of the economy
  • 3.1. The role of money in the reproduction process
  • 3.2. Differences in the characteristics of the role of money
  • 3.3. Features of the manifestation of the role of money in different models of the economy
  • Questions for self-control
  • Chapter 4. Issuance and release of money into economic circulation
  • 4.1. The concepts of "money issue" and "money issue". Forms of issue
  • 4.2. The essence and mechanism of the banking multiplier
  • 4.3. Issue of cash
  • Questions for self-control
  • Chapter 5. Money turnover. Its content and structure. Features of money turnover in different models of the economy
  • 5.1. The concept of "money circulation", its content and structure
  • 5.2. Features of money turnover in different models of the economy
  • 5.3. The relationship of money turnover with the system of market relations
  • Questions for self-control
  • Chapter 6. Cashless money circulation, its organization
  • 6.1. Fundamentals of the organization of money turnover
  • 6.2. Principles of organizing cashless payments
  • 6.3. Forms of cashless payments
  • 6.4. Payment Crisis and Directions for Its Mitigation in a Transition Economy
  • Questions for self-control
  • Chapter 7. Cash circulation, its organization. Monetary system
  • 7.1. The economic content of cash flow
  • 7.2. Organization of cash circulation
  • 7.3. Monetary systems, their forms and development
  • 7.4. The modern type of the monetary system, its characteristics
  • 7.5. Monetary unit and its purchasing power
  • 7.6. Directions of stabilization of the monetary unit
  • Questions for self-control
  • Chapter 8. Inflation
  • 8.1. Essence, forms of manifestation and causes of inflation, its socio-economic consequences
  • 8.2. Features of inflation in Russia
  • 8.2.1. Causes and forms of manifestation of inflation in the conditions of the planned distribution system
  • 8.2.2. Inflation in the context of the transition to market relations
  • Indicators of GDP decline rates compared to the previous year and inflation growth (%)
  • 8.2.3. The main directions of anti-inflationary policy
  • Questions for self-control
  • Section II.
  • 9.2. Introduction to the essence of credit
  • 9.3. The essence of the loan
  • 9.3.1. General requirements for the characterization of the essence of credit as an economic category
  • 9.3.2. Loan structure
  • 9.3.3. Stages of credit movement
  • 9.3.4. Loan basis
  • Questions for self-control
  • Chapter 10. Functions and laws of credit
  • 10.1. Loan functions
  • 10.2. Credit laws
  • Chapter 11. Forms and types of credit
  • 11.1. Loan forms
  • 11.2. Loan types
  • Chapter 12. The role of credit in the development of the economy, its boundaries
  • 12.1. The role of credit
  • 12.2. Changing the role of credit
  • 12.3. Loan limits
  • Questions for self-control
  • Chapter 13. Lending interest
  • 13.1. The nature of interest
  • 13.2. The economic basis for the formation of the level of loan interest
  • 13.3. Bank interest
  • Questions for self-control
  • Chapter 14. Interaction of credit and money
  • Chapter 15. Fundamentals of international monetary and financial relations
  • 15.1. Currency relations and currency system
  • 15.2. Balance of payments: concept and main items
  • Balance of payments structure:
  • 15.3. Exchange rate as an economic category
  • The state of the economy
  • Political situation in the country Degree of confidence in the currency in the national and world markets
  • 15.4. International payments
  • 15.5. International credit: essence and basic forms
  • 15.6. International financial flows and world markets
  • Questions for self-control
  • Section III.
  • 16.2. Characteristics of the elements of the banking system
  • 16.3. Banking system development
  • 16.4. The essence, functions and role of banks as an element of the banking system
  • 16.4.1. Modern ideas about the essence of the bank
  • 16.4.2. Methodological foundations of the analysis of the essence of the bank
  • 16.4.3. Functions and role of the bank
  • Questions for self-control
  • Chapter 17. The emergence and development of banks
  • 17.1. The emergence of banks
  • 17.1.2. Decentralization of the monetary economy, expansion of its basis and forms
  • 17.1.3. The emergence of stable forms of organization of the monetary and credit economy. Establishment of associations and partnerships
  • 17.1.4. Stabilization of forms and methods of regulation of the monetary and credit economy
  • 17.1.5. Features of the origin of banks in certain European countries
  • 17.2. Bank development
  • 17.2.1. External factors of consolidation of sustainable activities of banks
  • 17.2.2. Internal factors of consolidating the sustainable activities of banks
  • 17.2.3. Formation of a deposit base for sustainable banking activities
  • 17.2.4. The emergence of financial markets and the strengthening of the position of central banks
  • 17.2.5. Strengthening the trend of specialization and universalization of banking
  • Questions for self-control
  • Chapter 18. Features of modern banking systems. Creation of a two-tier banking system in Russia
  • 18.1. Features of building banking systems
  • 18.2. From the experience of organizing banking systems in foreign countries
  • 18.3. Features of building the banking system of Russia
  • Number of commercial banks
  • Questions for self-control
  • Chapter 19. Central banks
  • 19.1. General characteristics of central banks
  • 19.2. Tasks and functions of central banks
  • 19.3. Monetary regulation
  • Questions for self-control
  • Chapter 20. Commercial banks, their activities
  • 20.1. Commercial Bank Operations
  • 20.2. Banking services
  • 20.3. Problems of expanding the range of operations, liquidity and profitability of banks
  • Questions for self-control
  • Literature*
  • 13.3. Bank interest

    Bank interest is one of the most developed forms of loan interest in Russia. It occurs when one of the subjects credit relations the bank is speaking.

    The bank, like any lending institution, places in a loan, first of all, not its own, but borrowed funds. The share of the income received by the bank is compensation for intermediation, “risk pooling” and credit assessment. The risk of default on liabilities to the bank on its assets exceeds the risk of default on liabilities to the depositor. Thus, he assumes the risk of default on loans. In addition, depositors allow a lower interest rate on funds transferred to the bank so as not to search for clients and assess their creditworthiness.

    The level of bank interest on passive transactions, in addition to the general factors discussed in §13.2, depends on:

    The timing and size of the resources involved;

    Reliability commercial bank;

    The strength of the relationship with the client.

    The level of interest in the interbank money market, other things being equal, as a rule, exceeds the deposit interest rate, since it takes into account the costs and interests of the lending institution.

    The private factors underlying the determination of the level of interest on active operations of the bank include:

    Cost of loan capital;

    The borrower's creditworthiness;

    Purpose of the loan;

    The nature of the collateral;

    The term and volume of the loan provided.

    The upper limit of the interest on the loan is determined by market conditions. The lower limit is calculated taking into account the costs of the bank to raise funds and ensure the functioning of the credit institution.

    When calculating the rate of interest in each specific transaction, a commercial bank takes into account:

    Base interest rate level;

    Risk premium subject to the terms of the loan agreement.

    The base interest rate (Pbaz) is determined based on the approximate cost of credit investments and the pledged levels of profitability of the bank's lending operations for the coming period:

    Pbaz = C 1 + C 2 + P m ,

    where WITH 1 - the average real price of all credit resources for the planned period;

    WITH 2 - the ratio of the planned costs to ensure the functioning of the bank to the expected volume of productively allocated funds;

    P m - the planned level of profitability of the bank's lending operations with minimal risk.

    The average real price of credit resources (C 1) is determined by the weighted average arithmetic formula based on the price of a particular type of resource and its share in the total amount of funds mobilized by the bank (paid and free).

    The average real price of certain types of resources is determined on the basis of the market nominal price of the specified resources and adjustments for the rate mandatory reserve deposited with the Central Bank of the Russian Federation.

    In particular,

    where C - average real price of term deposits attracted by the bank;

    P - the average market level of the deposit interest.

    Similarly, the average real price is determined for other sources of funds, for which the deduction of funds to the required reserves fund is provided.

    The risk premium is differentiated depending on the following criteria:

    The borrower's creditworthiness;

    Availability of collateral for the loan;

    Loan term;

    The strength of the client's relationship with the bank.

    Considering that the interest on active operations of the bank plays an important role in the formation of income, and the payment of attracted resources occupies a significant place in the composition of its expenses, the problem of determining the interest margin is of current importance. (Mfact) those. the difference between the average rates on active (Pa) and passive operations of the bank (PP):

    Mfact = Pa - Pp

    The main factors affecting the size of the interest margin are the volume and composition of credit investments and their sources, the timing of payments, the nature of the applied interest rates and their movement.

    Under the current practice of lending in our country, as a rule, fixed interest rates are applied, which are not subject to revision until the end of the loan transaction. However, moving along the path of creating a market mechanism, one cannot ignore the experience of Western countries, where at the same time there is a set of interest rates, which, in most cases, are revised depending on the market situation and are adjusted to it.

    In these conditions, it is customary to divide all assets and liabilities into four categories in accordance with the speed of regulation of interest payments and the transition to a new level of rates. There is the following classification:

    A. Assets and liabilities that are subject to immediate and complete re-interest rate revaluations when market conditions change.

    B. Full regulation within three months.

    C. Assets and liabilities for which rates are revised in a period exceeding three months.

    D. Assets and liabilities with fully funded rates.

    The interaction of these factors is determined by comparing the first two categories of assets (A + B) with similar liabilities, taking into account the current market situation.

    During the period when interest rates rise, the bank is more favorable for the ratio when

    those. the number of assets with movable interest rates exceeds the corresponding amount of liabilities, and therefore the gap in rates on active and passive operations is widening - the interest margin is growing.

    On the contrary, when the market level of interest falls, it is advisable to adhere to the following ratio when

    and underpin assets with fixed rates due to liabilities characterized by the urgency of the revision of interest payments.

    For effective management of income from lending operations, the minimum interest margin is determined and analyzed, which characterizes the existing amount of costs not covered by received commissions and other income, for each ruble of productively allocated funds:

    where P b- expenses for ensuring the functioning of the bank (all expenses, except for the amounts of accrued interest);

    D P- other income of the credit institution (income, excluding income from active operations of the bank); reimbursement by customers of postage and telegraph costs, received payments for services rendered to enterprises, interest and commissions received in addition in previous years, and demanded interest and commissions overpaid to customers in previous years, other income;

    A - the asset of the bank's balance sheet, which generates income on invested funds: loan investments acquired securities, funds transferred to enterprises to participate in their economic activities, etc.

    The above approaches are used by commercial banks when conducting an interest rate policy on active and passive operations.

    Bank interest. Interest margin

    Bank interest is one of the most developed forms of loan interest in Russia. It arises when a bank acts as one of the subjects of credit relations.

    The bank does not lend own funds, and attracted. The share of the income received by the bank is compensation for intermediation.

    The level of bank interest on passive transactions depends on (deposit interest):

    The timing and size of the resources involved;

    The reliability of a commercial bank;

    The strength of the relationship with the client.

    The level of bank interest on active operations (lending) depends on:

    The borrower's creditworthiness;

    The purpose of the loan;

    The nature of ensuring the repayment of funds;

    The term and volume of the loan provided.

    Upper bound interest on the loan is determined by market conditions.

    Bottom line interest for a loan is determined by the bank's costs of raising funds and ensuring the functioning of a credit institution.

    When calculating the rate of interest for each credit transaction, the bank takes into account:

    Base interest rate level;

    Risk premium subject to the terms of the loan agreement.

    Considering that the interest on the active operations of the bank plays an important role in the formation of income, and the payment for attracted resources occupies a significant place in the composition of its expenses, the problem of determining interest margin(Mfact)

    Mfact represents the difference between the average rates on active (Pa) and passive (Pp) operations:

    Mfact = Pa-Pp

    Interest rate- it relative magnitude interest payments on loan capital for a certain period of time (usually a year). It is calculated as the ratio of the absolute amount of interest payments for the year to the amount of loan capital.

    Fixed interest rate- is established for the entire period of use of borrowed funds without a unilateral right to revise it.

    Floating interest rate- This is the rate on medium and long-term loans, which consists of two parts: a movable basis, which changes in accordance with market conditions and a fixed amount, usually unchanged throughout the entire period of lending or circulation of debt securities.

    Types of interest rates:

    1. Refinancing rate - This is the official rate of lending to commercial banks from the Central Bank of the Russian Federation.

    The refinancing rate is one of the main instruments by which central banks regulate volumes money supply in circulation.

    Refinancing of commercial banks is carried out through direct short-term lending the central bank.



    A decrease in the official refinancing rate leads to a decrease in the cost of credit resources and an increase in their supply in the market. An increase in the discount rate leads to a contraction of the money supply, a slowdown in inflation, but at the same time to a reduction in investment.

    2. Bank interest rate on loans - the rate of interest on credit operations, one side of which is the bank.

    As a rule, the bank places in a loan, first of all, not its own, but borrowed funds.

    The share of the income received by the bank represents compensation for intermediation, the risk of default and the assessment of the borrower's creditworthiness.

    When determining the rate of interest for each specific transaction, a commercial bank takes into account:

    Base interest rate level;

    Risk premium.

    The base interest rate (Pbaz) is determined based on the planned "cost" of loan capital and the pledged level of profitability of the bank's lending operations for the coming period:

    Pbaz = C 1 + C 2 + M p,

    where Пбаз is the base interest rate;

    С 1 - the average real price of all credit resources for the planned period (rate on attracted funds, including funds attracted in deposits);

    С 2 - the ratio of the planned expenses to ensure the work of the bank to the expected volume of productively allocated funds (the share of the bank's expenses in the unit of allocated funds);

    M p - the planned level of profitability of the bank's lending operations.

    The average real price of funds attracted by the bank (credit resources) С 1 is determined by the weighted average formula based on the price of a particular type of resources (С j) and its share in the total amount of funds mobilized by the bank (paid and free).

    С j are set on the basis of the market nominal price of these resources and adjustments for the rate of the required reserve deposited with the Central Bank:

    The risk premium is differentiated depending on the following main criteria:

    Borrowers' creditworthiness;

    Availability of collateral for the loan;

    Loan term;

    The strength of the client's relationship with the bank and credit history client.

    That. the upper limit of the interest on the loan is determined by market conditions. The lower limit is calculated taking into account the bank's costs to raise funds and ensure the functioning of the bank.

    Types of interest rates

    Simple interest rate- applies to the same initial amount of debt throughout the entire loan term, i.e. the original base (amount of money) is always the same.

    Compound interest rate- applies to the accrued or reduced amount of debt, i.e. to the amount changed by the amount of interest accrued for the previous period. That. the initial basis for calculating interest is constantly changing (interest is calculated on the amount received at the previous stage of accrual or discounting).

    When calculating interest from the present to the future, the build-up rate.

    When calculating interest from the future to the present, apply discount rates or discount rates.

    The interest received at the accrual rate is called decursive.

    The interest earned at the discount rate is called antisipative.

    - interest rate (accrual rate);

    where FV is the future value of the current amount of money;

    PV is today's value for money.

    Discount rate.


    Compound interest formula:

    - for one period of accrual

    - for two periods of accrual

    Influence of inflation on the size of simple interest rates:

    Let the capital PV be charged with simple interest at the rate r during time n and the price index for this time is equal to I (n), then, taking into account the depreciation of money during this time, we get:

    where is the multiplier of the build-up by a simple percentage of inflation.

    It follows from the formula that the real increase in the initial capital, taking into account the purchasing power of money, will be only if 1 + ni> I (n)

    If 1 + ni = I (n), then the increase only compensates for the effect of inflation

    From the equality 1 + ni = I (n), we find r

    where i * is the minimum permissible interest rate at which there is no real reduction in capital (capital erosion).

    The rate exceeding i * is called positive interest rate since only when it is applied will there be a real increase in capital.

    Gross - rate (i /)- interest rate, indexed taking into account the growth of the price level to take into account inflation

    To ensure full compensation for the negative impact of inflation and profitability in accordance with original rate i, gross amount - bet i / is determined from the equality

    If the gross rate is set i / (i.e. the rate of return is declared), then the real interest rate can be determined, i.e. rate of return adjusted for inflation when calculating simple interest

    That. under inflation distinguish the following types interest rates

    Nominal interest rate Is the original base (usually annual) interest rate specified in the contracts. The yield expressed by this rate is not adjusted for inflation.

    Real interest rate- shows the profitability taking into account inflation, characterized by a decrease in the purchasing power of money. In conditions of inflation, it is always less than the nominal interest rate and may even be negative.

    Positive interest rate is any rate at which there will be a real increase in the cost of capital for a given inflation index.

    Gross - interest rate- the interest rate, indexed taking into account the rise in the price level to take into account inflation (the rate at which capital actually grows with necessary profitability) .

    In conditions of galloping inflation (15-20% per year), a floating interest rate is also used.

    When calculating interest on deposits and loans for up to a year, a formula is applied, which can be written as:

    where t k is the duration in days of the period for which the interest rate r k is set,

    T is the number of days in a year.

    The magnitude discount rate d /, which compensates for inflationary losses, is determined from the equality:

    If the rate d / is set, then from the last equality it is possible to determine the real discount rate, which makes it possible to estimate accordingly the rate of return in case of inflation

    If the price index is less than one, then this indicates deflation.

    Influence of inflation on the size of compound interest rates:

    Let the PV capital be charged with compound interest for n years and the price index for this time is equal to

    FV = PV * c n, = PV * c n.

    where m is the number of charges per year.

    But adjusted for inflation:

    Hence, it is clear that in order to avoid capital erosion, the inequality with n ≥I (n) must be fulfilled, which is equivalent to the inequality

    and if, then the increase in capital only neutralizes the effect of inflation.

    A bet for which the corresponding coefficient c is greater than c * is called a positive bet.

    For example, if, then the positive interest rate is determined from the inequality, which implies

    If for n years the expected annual inflation rate is I, then I = 1 + h, I (n) = (I) n = (1 + h) n, where h is the expected annual inflation rate.

    If compound interest is calculated once a year, then i (m) = i> h, i.e. the interest rate must be higher than the inflation rate.

    Assuming that, we find that the positive discount rate satisfies the inequality, and for m = 1 and I (n) = (1 + h) n we get

    To ensure a real growth in the cost of initial capital, it is necessary to increase (index) the initial rate. The choice of the value of such an indexed rate, called the gross rate, is determined by the goals set.

    To ensure real profitability according to the growth rate c, it is necessary to index the original rate (increase by the inflation premium) so that the new growth rate c / fully compensates for losses due to inflation. Thus, c / is determined from the equality:

    r wsp: rsidR = "00000000"> "> , Þ

    The size of the gross rate (i /) provides full compensation for the negative impact of inflation and obtaining profitability. Therefore, in the formula (*), the factor with n must be equated to the factor, then if

    - gross build-up rate

    By specifying the gross rate in the formula (**), you can determine the real rate of increase i (m) (express from (**) i (m))

    Real build rate

    We derive formulas for determining the real gross rate d / (m) and the real discount rate d (m)

    If, then taking into account (*)

    Discount gross rate

    From the formula (***), one can express the real discount rate d (m)

    Real discount rate

    Fisher I.

    For I (n) = (1 + h) n and m = 1 from (**) i (1) / = i / we obtain (denoting i (1) = i)

    where h + ih is the inflation premium to be added to the original rate of return to compensate for inflationary losses

    formula output:

    3. Deposit rate on passive operations of banks

    The deposit rate is always lower than the credit one by several points.

    Spread (or interest margin) - the difference between the credit and deposit rates. The spread covers the costs of maintaining the bank and generates profit.

    Minimum interest margin (Мmin). For effective management of income from loan operations, Mmin is determined and analyzed. Mmin characterizes the existing amount of costs not covered by received commissions and other income, for each ruble of productively allocated funds:

    Mmin = (RB - DP): Arab * 100%,

    where Рб - expenses to ensure the work of the bank; 9 all expenses, except for the amounts of accrued interest);

    Дп - other income of the credit institution (income, excluding income from active operations): received payment for services rendered to enterprises, interest and commissions received in addition in previous years, other income;

    Arab is an asset of the bank's balance sheet, generating income on invested funds: credit investments, securities in the portfolio, funds transferred to enterprises to participate in their economic activity and etc.

    4. Interbank interest rate

    Interest rate on loans in the interbank market (wholesale market of credit resources)

    LIBOR (London InterBank Offered Rate) is a scale of interest rates that are used by London banks operating in the Euro-currency interbank market offering funds in different currencies and for different periods: 1,2,6 and 12 months.

    Each major London bank independently sets and changes the LIBOR rate depending on market conditions. In a narrow sense, it is the average interest rate on the supply of funds by the largest UK banks. Traditionally, LIBOR rates have been used as a “rolling basis” for lending on a floating rate basis.

    In Russia, there are the following aggregate rates of the interbank market:

    MIBOR (Moskow InterBank Offered Rate) - an offer for sale - the average interest rate of the rates of placement of interbank loans announced daily by the largest Moscow banks.

    MIBID (Moskow InterBank Bid) - offer to buy - the average interest rate of the daily rates for attracting interbank loans announced by the largest Moscow banks (the rate at which banks are ready to buy interbank loans)

    MIACR (Moskow InterBank Actual Credit Rate) is the average weighted interest rate on the volume of actual transactions on the provision of interbank loans by commercial banks (the average actual rate on the provision of loans)

    Interest on bank loans- payment received by the lender (bank) from the borrower for the use of borrowed funds (loan). Granting loans is financial transaction, which provides for the provision of a loan of a certain amount of money (A o) with the condition that after a specified time the borrower will return a large amount (A 1) with an increment in the form of interest. The creditor's income is usually called interest income.

    Accrual period, amount, term and procedure for paying interest on different types loan operations are established under a loan agreement between the bank and the borrower.

    At the level of interest rates commercial bank affect: the average level of payment for attracted resources, i.e. deposit interest; bank expenses; purpose (object) of lending; the customer's creditworthiness; the nature of the client; the degree of riskiness of the project; the level of the tax rate on the bank's income; the state of demand for credit; loan term; the possibility of additional attraction of credit resources (availability, offers, amount of payment); inflation rate and other factors arising from monetary policy central bank, government, creditor and borrower image.

    The interest rate also depends on the risk of the borrower's insolvency; the nature of the security provided; return guarantees; the content of the credited event; rates of competing banks and other factors. The interest rate on the loan may also include the fee for the services rendered to the borrower when issuing a loan.

    The upper limit of the interest on the loan is determined by market conditions. The lower limit is calculated taking into account the bank's costs of raising funds with the addition of a margin that ensures the functioning of the credit institution. When calculating the rate of interest in each specific transaction, a commercial bank takes into account the level of the base interest rate and the risk premium, taking into account the loan agreement. Base interest rate is determined based on the estimated cost of credit investments and the pledged level of profitability of the bank's lending operations with minimal risk. The approximate cost of credit investments includes the average real price of all credit resources for the planned period plus the bank's planned expenses to ensure its functioning (the ratio of expenses to the expected volume of credit investments). The average real price of credit resources is determined on the basis of their market nominal price and adjustment for the rate of the required reserve deposited with the central bank.

    The base (base) rate for a loan is the result of the average impact of factors on the level of rates. This is not a minimum rate, as banks can provide loans at a lower interest rate. The base rate may vary from bank to bank. When setting the percentage, banks usually take into account the size of the base interest rate from other banks. Many small banks can change the interest for a commercial loan depending on the base rate of the large banks. The base rate is a kind of starting, or starting amount.

    The percentage on active operations of the bank plays an important role in the formation of income, and the payment for resources occupies a significant place in the composition of its expenses, therefore, the correct determination of the margin is of particular importance.