Real and nominal interest rates. Nominal interest rate The nominal interest rate is

The most important characteristic of the modern economy is the depreciation of investments through inflationary processes. This fact makes it advisable to use not only a nominal, but also a real interest rate when making some decisions in the market. What is an interest rate? What does it depend on? How ?

Interest rate concept

The interest rate should be understood as the most important economic category that reflects the profitability of any asset in real terms. It is important to note that it is the interest rate that plays a decisive role in the process of making management decisions, because any economic entity is very interested in obtaining the maximum level of revenue at minimum costs in the course of its activities. In addition, each entrepreneur, as a rule, reacts to the dynamics of the interest rate in an individual way, because in this case the determining factor is the type of activity and the industry in which, for example, the production of a particular company is concentrated.

Thus, owners of capital assets often agree to work only if the interest rate is extremely high, and borrowers are likely to acquire capital only if the interest rate is low. The examples discussed are clear evidence that today it is very difficult to find equilibrium in the capital market.

Interest rates and inflation

The most important characteristic of a market economy is the presence of inflation, which determines the classification of interest rates (and, naturally, the rate of return) into nominal and real. This allows you to fully assess the effectiveness of financial transactions. If the inflation rate exceeds the interest rate received by the investor on investments, the result of the corresponding operation will be negative. Of course, in terms of absolute value, his funds will increase significantly, that is, for example, he will have more money in rubles, but the purchasing power that is characteristic of them will drop significantly. This will lead to the opportunity to buy only a certain amount of goods (services) with the new amount, less than would have been possible before the start of this operation.

Distinctive features of nominal and real rates

As it turned out, they differ only in conditions of inflation or deflation. Inflation should be understood as a significant and sharp decline, while deflation should be understood as a significant drop. Thus, the nominal rate is considered to be the rate set by the bank, and the purchasing power inherent in income and denoted as interest. In other words, the real interest rate can be defined as the nominal interest rate, which is adjusted for inflation.

Irving Fisher, an American economist, formed a hypothesis explaining how it depends on nominal values. The main idea of ​​the Fisher effect (this is the name of the hypothesis) is that the nominal interest rate tends to change in such a way that the real one remains “stationary”: r(n) = r(p) + i. The first indicator of this formula reflects the nominal interest rate, the second - the real interest rate, and the third element is equal to the expected rate of inflation processes, expressed as a percentage.

The real interest rate is...

A striking example of the Fisher effect, discussed in the previous chapter, is the picture when the expected rate of the inflation process is equal to one percent on an annual basis. Then the nominal interest rate will also increase by one percent. But the real percentage will remain unchanged. This proves that the real interest rate is the same as the nominal interest rate minus the expected or actual inflation rate. This rate is completely free of inflation.

Calculation of the indicator

The real interest rate can be calculated as the difference between the nominal interest rate and the level of inflation processes. Thus, the real interest rate is to the following relation: r(р) = (1 + r(н)) / (1 + i) - 1, where the calculated indicator corresponds to the real interest rate, the second unknown member of the relationship determines the nominal interest rate, and the third element characterizes the inflation rate.

Nominal interest rate

When talking about lending rates, as a rule, we are talking about real rates ( the real interest rate is purchasing power of income). But the fact is that they cannot be observed directly. Thus, when concluding a loan agreement, an economic entity is provided with information about nominal interest rates.

The nominal interest rate should be understood as a practical characteristic of interest in quantitative terms, taking into account current prices. The loan is issued at this rate. It should be noted that it cannot be greater than zero or equal to it. The only exception is a loan on a free basis. Nominal interest rate is nothing more than interest expressed in monetary terms.

Calculation of the nominal interest rate

Suppose an annual loan of ten thousand monetary units pays 1,200 monetary units as interest. Then the nominal interest rate is equal to twelve percent per annum. After receiving 1200 monetary units on a loan, will the lender become rich? This question can be answered correctly only by knowing exactly how prices will change over the course of an annual period. Thus, with annual inflation equal to eight percent, the lender's income will increase by only four percent.

The nominal interest rate is calculated as follows: r = (1 + percentage of income received by the bank) * (1 + increase in inflation rate) - 1 or R = (1 + r) × (1 + a), where the main indicator is the nominal interest rate, the second is the real interest rate, and the third is the growth rate of the inflation rate in the country corresponding to the calculations .

conclusions

There is a close relationship between nominal and real interest rates, which for absolute understanding it is advisable to present as follows:

1 + nominal interest rate = (1 + real interest rate) * (price level at the end of the time period under consideration / at the beginning of the time period under consideration) or 1 + nominal interest rate = (1 + real interest rate) * (1 + rate of inflation processes).

It is important to note that the real effectiveness and efficiency of transactions performed by the investor is reflected only by the real interest rate. It talks about the increase in funds of a given economic entity. The nominal interest rate can only reflect the increase in funds in absolute terms. It does not take inflation into account. Increase in real interest rate speaks of an increase in the level of purchasing power of the monetary unit. And this equals the opportunity to increase consumption in future periods. This means that this situation can be interpreted as a reward for current savings.

The interest rate is one of the most important macroeconomic indicators. There are many different interest rates in the financial market. First of all, interest rates on deposits and loans differ. For example, at the end of June 2012, rates on ruble deposits of individuals in Sberbank of Russia were in the range of 0.01-8.75% per annum, and rates on loans for the purchase of real estate in the same bank were in the range of 11-16.5% per annum. Sberbank's interest rates differ from rates in other commercial banks and rates in the interbank lending market. Interest rates in the banking system as a whole may differ from interest rates (or similar amounts, such as annual stock returns) in other segments of the financial market, such as private or government securities markets. Additionally, the size of the rates may be influenced by different degrees of investment risk in different segments of the financial market (a higher risk corresponds to a higher percentage). However, interest rate movements in different segments of the financial market are driven by similar mechanisms, and in most cases the broad spectrum of interest rates in a country moves in the same direction (barring short-term fluctuations). Therefore, in the future, by interest rate we will understand a certain single, abstract, “average” interest rate.

The importance of the interest rate lies primarily in the fact that it characterizes the cost of using borrowed funds in the financial market. Rising interest rates mean that borrowing from the financial market will become more expensive and less accessible to potential borrowers - for example, firms wanting to expand their business and upgrade their equipment, or home buyers wanting to get a mortgage. If rising interest rates force them to abandon investments, this could have far-reaching undesirable consequences for the entire economic system of the country. What could cause interest rates to rise? One of the reasons is increased inflation (especially in modern Russia). To describe the relationship between interest rates and inflation, it is necessary to introduce the concepts of real and nominal interest rates.

The typical interest rate that you might see when you go to a bank or other financial institution is called nominal (g). The nominal rates on deposits and loans at Sberbank in June 2012, given above. It is interesting that in 1992 in the same bank the interest rate on deposits (in rubles) could reach 190% per annum. Thus, every ruble placed on this deposit at the beginning of 1992 turned into 2 rubles over the year. 90 kopecks (1 ruble of the original deposit plus 190%). But did the owner of the deposit become richer as a result? Suppose at the beginning of 1992 for 1 rub. you could buy one loaf of bread. According to official statistics, in 1992 the inflation rate in Russia was approximately 2540%. If bread rose in price at such a rate, then its price over the year increased 26.4 times (see mathematical commentary “Growth and Increment Rates”) and by the end of the year amounted to 26 rubles. 40 kopecks Thus, at the beginning of the year, 1 ruble deposited could buy one loaf of bread. At the end of the year, for the 2 rubles received from the bank. 90 kopecks it was possible to buy only approximately one tenth of this loaf (to be precise, 2 rubles 90 koi: 26 rubles 40 koi "0.11 loaves of bread). Due to the fact that the growth in the size of the deposit in the bank lagged behind the rise in prices, the depositor lost nine-tenths of a loaf of bread, or, in other words, nine-tenths of the purchasing power of his money (to be precise, he lost 89% of its purchasing power, i.e. from one whole loaf at the beginning of the year there was only 0.11 loaves left at the end of the year and) The value -89%, in the calculation of which the nominal interest rate was adjusted for the inflation rate, is called real interest rate. It is usually denoted by the small letter r . Given data on the nominal interest rate i and the inflation rate π, the real interest rate can always be calculated using the Fisher formula:

(here all three values ​​are expressed as percentages). An example of using Fisher's formula for our 1992 data:

If the inflation rate in the country is insignificant,

a simpler, approximate formula can be used that relates nominal, real interest rates and the inflation rate:. For example, if the annual inflation rate π was 1%, and the nominal rate i was equal to 3%, then the real interest rate was approximately

Let's return to the previously asked question, slightly modifying it. Why do nominal interest rates change? From the formula we find the nominal rate: . We get an effect called Fisher effect. In accordance with this effect, two main components of the nominal interest rate are distinguished - real interest and the inflation rate and, accordingly, two reasons for its change. Typically, a financial institution (say, a bank), when determining the nominal interest rate for the next year, proceeds from some target value of the real rate and its expectations regarding the future rate of inflation. If the target value of the real rate is +2% per annum and the bank’s experts expect a price increase over the next year of 1.5%, then the nominal rate will be set at 3.5% per annum. Please note that in this example, the formation of the nominal interest rate was influenced not by actual, but by expected inflation, which can be formalized as , where is the expected inflation rate (e - from English expected, expected).

Thus, the nominal rate is determined by two components - the real rate and the expected inflation rate. Note that fluctuations in the real interest rate are usually less significant than fluctuations in the expected inflation rate. In this case, according to the Fisher effect the dynamics of the nominal interest rate is largely determined by the dynamics of the expected inflation rate(Fig. 2.13 is offered as an illustration).

In turn, expected inflation is largely determined by the past history of this economic indicator: if inflation was insignificant in the past, it is expected that it will be insignificant in the future. If a country has previously experienced severe inflation, this gives rise to pessimistic expectations for the future. If in Russia until recently the inflation rate, as a rule, was a double-digit value, this also had an impact on the average interest rates in our country, and increased inflation led to an increase in funeral interest rates, and weakening inflation slightly reduced them.

Rice. 2.13.

The interest rate is indicated for 3-month Treasury bills; inflation is calculated as the growth rate of the CPI for All Urban Consumers in a given month relative to the same month last year. Sources: According to the US Federal Reserve (federalreserve.gov) and the US Bureau of Labor Statistics (bls.gov).

Financial institutions try to attract the attention of customers by offering favorable interest rates on deposits. At first glance, the yield values ​​are very attractive in a number of cases. Investing your savings at rates above 12% is currently an ultra-generous proposition. However, everyone sees the interest rate numbers in large, bright font, and few people read the text written in small font at the bottom. Banks declare only the nominal income that the depositor will receive after a specified period. They never mention the concept of “real income,” which is what the client actually receives. Let's take a closer look at what the nominal and real deposit rates are, how they differ, what are their similarities, and how to calculate real income?

What is the nominal interest rate on a deposit?

The nominal deposit rate is the value of the nominal income that the depositor will receive after the period established by the agreement. This is what banks indicate when attracting clients to place deposits. It does not reflect the investor’s real income, which he will receive taking into account the depreciation of money (or inflation) and other expenses. Thus, the nominal interest on the deposit is determined by several components:

• Real interest rate.
• Expected inflation rate.
• Other expenses of the depositor, including personal income tax for the difference in the excess rate from the refinancing rate increased by 5 percentage points), etc.

Of all the components, the rate of annual inflation shows the greatest fluctuations. Its expected value depends on historical fluctuations. If inflation consistently shows low values ​​(0.1-1%, as in the West or the USA), then in future periods it is set at approximately the same level. If the state experienced high inflation rates (for example, in the 90s in Russia this figure reached 2500%), then bankers set a high value for the future.

What is the real deposit rate?

The real interest rate is interest income adjusted for inflation. Its value is usually not indicated anywhere by banks. The client can calculate it independently or rely on the bank’s honest attitude towards him.

The real income from investing money on a deposit is always less than the nominal one, since it takes into account the amount that will be obtained after adjusting for inflation. The real rate reflects the purchasing power of money upon expiration of the deposit term (i.e., more or fewer goods can be purchased for the final amount compared to the initial amount).

Unlike nominal interest, real interest can also have negative values. The client will not only not save his savings, but will also receive a loss. Developed countries deliberately keep real rates negative to stimulate economic development. In Russia, real rates change from positive to negative, especially recently.

How to calculate the real interest rate on a deposit?

To start the calculation, you need to determine all the investor's expenses. These include:

• Tax. For deposits there is a 13% personal income tax. It applies if the nominal interest on ruble deposits is 5 percentage points higher than the SR. (until December 31, 2015, the conditions apply that personal income tax will be levied on deposits with a rate higher than 18.25%). The accrued tax will be automatically deducted by the bank when issuing the accumulated amount to the depositor.
• Inflation. As the amount of savings increases, the price of goods and services also increases. As of May 2015, inflation was estimated at 16.5%. At the end of the year, its predicted value is estimated at 12.5% ​​(taking into account the stabilization of the economic situation).

Let's look at example 1.

The investor managed to place 100 thousand rubles at the beginning of the year. at 20% per annum for 1 year without capitalization with interest payment at the end of the term. Let's calculate his real income.

Nominal income (NI) will be:

100,000+(100,000*20%) = 120,000 rub.

Real income:

RD = ND - Tax - Inflation

Tax = (100,000 * 20% - 100,000 * 18.25%) * 13% = 227.5 rubles.

Inflation=120,000*12.5% ​​= 15,000 rubles.

Real income = 120,000 -227.5-15,000 = 104,772.5 rubles.

Thus, the depositor actually increased his wealth by only 4,772 rubles, and not by 20,000 rubles, as stated by the bank.

Let's look at example 2.

The investor placed 100 thousand rubles. at 11.5% per annum for 1 year with interest payment at the end of the deposit term. Let's calculate his real profit.

The nominal profit will be:

100,000+(100,000*11.5%) = 111,500 rub.

Tax=0, because interest rate below SR+5 pp.

Inflation = 111,500 * 12.5% ​​= 13,937.5 rubles.

Real income = 111,500 - 13,937.5 = 97,562.5 rubles.

Loss = 100,000 - 97,562.5 = 2437.5 rubles.

Thus, under these conditions, the purchasing power of the depositor's savings turned out to be negative. Not only was he unable to increase his savings, but he also lost some.

• You should always calculate your real income when investing in deposits.
• You need to invest at an interest rate that is higher than the inflation rate. Otherwise, the growth of savings will not keep pace with the rise in prices.
• You should not trust banks that offer extremely high interest rates. This indicates his poor condition.

a) an interest rate established without taking into account changes in the purchasing value of money due to inflation (or a general interest rate in which its inflationary component is not eliminated);

B) the interest rate on a fixed income security that refers to the par value rather than the market price of the security.

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Real interest rate

REAL INTEREST RATE

(real interest rate) The actual interest rate minus the current inflation rate. For example, if a building society pays out 5% and the inflation rate is 3%, the real increase in deposits placed with the building society over the year is 2%, which is the real interest rate. Real interest rates are used to calculate the return on invested capital, taking into account inflation.

Finance. Dictionary. 2nd ed. - M.: "INFRA-M", Publishing House "Ves Mir". Brian Butler, Brian Johnson, Graham Sidwell and others. General editor: Ph.D. Osadchaya I.M.. 2000 .

Real interest rate

The real interest rate is the interest rate net of inflation. The real interest rate is calculated as the difference between the nominal interest rate and the inflation rate. There are:
- ex ante - expected real interest rate at the time of loan issuance;
- ex post - the actual real interest rate.

In English: Real interest rate

See also: Interest rates

Finam Financial Dictionary.

Real interest rate

The actual interest rate minus the current inflation rate. For example, if a bank pays 5% and the inflation rate is 3%, the real increase in deposits placed with the bank over the year is 2%, which is the real interest rate. Real interest rates are used to calculate the return on invested capital, taking into account inflation.

Terminological dictionary of banking and financial terms. 2011 .

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