What is the real interest rate. Nominal interest rate

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 is applied 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.

Percentage is absolute value. For example, if 20,000 is borrowed and the debtor must return 21,000, then the interest is 21,000-20,000=1000.

The lending interest rate (norm) - the price for using money - is a certain percentage of the amount of money. Determined at the point of equilibrium between the supply and demand of money.

Very often in economic practice, for convenience, when they talk about loan interest, they mean the interest rate.

There are nominal and real interest rates. When people talk about interest rates, they mean real interest rates. However, actual rates cannot be directly observed. By concluding a loan agreement, we receive information about nominal interest rates.

Nominal rate (i)- quantitative expression of the interest rate taking into account current prices. The rate at which the loan is issued. The nominal rate is always greater than zero (except for a free loan).

Nominal interest rate- This is a percentage in monetary terms. For example, if for an annual loan of 10,000 monetary units, 1,200 monetary units are paid. as interest, the nominal interest rate will be 12% per annum. Having received an income of 1200 monetary units on a loan, will the lender become richer? This will depend on how prices have changed during the year. If annual inflation was 8%, then the lender’s income actually increased by only 4%.

Real rate(r)= nominal rate - inflation rate. The real bank interest rate can be zero or even negative.

Real interest rate is an increase in real wealth, expressed as an increase in the purchasing power of the investor or lender, or the exchange rate at which today's goods and services, real goods, are exchanged for future goods and services. The fact that the market rate of interest would be directly influenced by inflationary processes was the first to suggest I. Fischer, which determined the nominal interest rate and the expected inflation rate.

The relationship between the rates can be represented by the following expression:

i = r + e, where i is the nominal, or market, interest rate, r is the real interest rate,

e - inflation rate.

Only in special cases, when there is no price increase in the money market (e = 0), do real and nominal interest rates coincide. The equation shows that the nominal interest rate can change due to changes in the real interest rate or due to changes in inflation. Since the borrower and lender do not know what rate inflation will take, they proceed from the expected rate of inflation. The equation becomes:

i = r + e e, Where e e expected inflation rate.

This equation is known as the Fisher effect. Its essence is that the nominal interest rate is determined not by the actual rate of inflation, since it is unknown, but by the expected rate of inflation. The dynamics of the nominal interest rate repeats the movement of the expected inflation rate. It must be emphasized that when forming a market interest rate, it is the expected inflation rate in the future, taking into account the maturity of the debt obligation, that matters, and not the actual inflation rate in the past.

If unexpected inflation occurs, then borrowers benefit at the expense of lenders, since they repay the loan with depreciated money. In the event of deflation, the lender will benefit at the expense of the borrower.

Sometimes a situation may arise where real interest rates on loans are negative. This can happen if the inflation rate exceeds the growth rate of the nominal rate. Negative interest rates can be established during periods of runaway inflation or hyperinflation, as well as during an economic downturn, when demand for credit falls and nominal interest rates fall. Positive real interest rates mean higher income for lenders. This occurs if inflation reduces the real cost of borrowing (credit received).

Interest rates can be fixed or floating.

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

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

Quite often you can see, at first glance, lucrative offers that promise financial independence. These could be bank deposits or opportunities for investment portfolios. But is everything as profitable as the advertisement says? We will talk about this in the article, finding out what the nominal rate and the real rate are.

Interest rate

But first, let's talk about the basis of the basics in this matter - the interest rate. It represents the nominal benefit that a certain person can receive when investing in something. It should be noted that there are quite a few possibilities of losing your savings or the interest rate that a person should receive:

Therefore, it is necessary to study in great detail what you are going to invest in. It should be remembered that the interest rate is often a reflection of the riskiness of the project being studied. Thus, those that offer a return level of up to 20% are considered the safest. The high-risk group includes assets that promise up to 70% per annum. And anything greater than these indicators is a danger zone into which you should not venture without experience. Now that there is a theoretical basis, we can talk about what the nominal rate and the real rate are.

The concept of a nominal rate

Defining nominal is very simple - it is understood as the value given to market assets and evaluates them without taking into account inflation. An example would be you, the reader, and a bank that offers a deposit at 20% per annum. For example, you have 100 thousand rubles and want to increase them. So they put it in the bank for one year. And after the deadline, they took 120 thousand rubles. Your net profit is as much as 20,000.

But is it really like that? After all, during this time the price of food, clothing, and travel could have risen significantly - and, say, not by 20, but by 30 or 50 percent. What to do in this case to get a real picture of things? What should you still give preference to when given the opportunity to choose? What should be chosen as a guideline for yourself: the nominal rate and the real rate or one of them?

Real rate

For such cases, there is such an indicator as the real rate of return. It is noteworthy that it can be calculated quite easily. To do this, subtract the expected inflation rate from the nominal rate. Continuing the example given earlier, we can say this: you deposited 100 thousand rubles in the bank at 20% per annum. Inflation was only 10%. As a result, the net nominal profit will be 10 thousand rubles. And if you adjust their cost, then 9,000 according to last year’s purchasing opportunity.

This option allows you to receive, albeit insignificant, profit. Now we can consider another situation in which inflation was already 50 percent. You don’t need to be a mathematical genius to understand that the state of affairs forces you to look for some other way to save and increase your funds. But so far this has all been in the style of simple description. In economics, the so-called Fisher equation is used to calculate all this. Let's talk about it.

Fisher's equation and its interpretation

It is possible to talk about the difference between the nominal rate and the real rate only in cases of inflation or deflation. Let's look at why. The idea of ​​the relationship between nominal and real rates and inflation was first put forward by economist Irving Fisher. In the form of a formula, everything looks like this:

NS=RS+OTI

NS is the nominal interest rate of return;

OTI - expected inflation rate;

RS is the real bet.

The equation is used to describe the Fisher effect mathematically. It sounds like this: the nominal interest rate always changes by an amount at which the real one remains unchanged.

It may seem complicated, but now let's take a closer look. The fact is that when the expected value is 1%, the denomination also increases by 1%. Therefore, it is impossible to create a quality investment decision-making process without taking into account the differences between rates. Previously, you only read about the thesis, but now you have mathematical proof that everything described above is not a simple fiction, but, alas, a sad reality.

Conclusion

What can we say in conclusion? Whenever you have a choice, you need to take a quality approach to choosing an investment project for yourself. It doesn’t matter what it is: a bank deposit, participation in a mutual investment fund or something else. And to calculate future income or possible losses, always use economic tools. So, the nominal interest rate may promise you a pretty good profit now, but when assessing all the parameters, it will turn out that not everything is so rosy. And economic tools will help you calculate which decision will be the most profitable.

Percent is an absolute value. For example, if 20,000 is borrowed and the debtor must return 21,000, then the interest is 21,000-20,000=1000.

Loan interest rate (norm)– the price for using money is a certain percentage of the amount of money. Determined at the point of equilibrium between the supply and demand of money.

The interest rate is .

Very often in economic practice, for convenience, when they talk about loan interest, they mean the interest rate.

There are nominal and real interest rates. When people talk about interest rates, they mean real interest rates. However, actual rates cannot be directly observed. By concluding a loan agreement, we receive information about nominal interest rates.

Nominal rate(i)– quantitative expression of the interest rate taking into account current prices. The rate at which the loan is issued. The nominal rate is always greater than zero (except for a free loan).

Nominal interest rate is a percentage in monetary terms. For example, if for an annual loan of 10,000 monetary units, 1,200 monetary units are paid. as interest, the nominal interest rate will be 12% per annum. Having received an income of 1200 monetary units on a loan, will the lender become richer? This will depend on how prices have changed during the year. If annual inflation was 8%, then the lender’s income actually increased by only 4%.

Real rate(r)= nominal rate – inflation rate. The real bank interest rate can be zero or even negative.

Real interest rate is an increase in real wealth, expressed as an increase in the purchasing power of the investor or lender, or the exchange rate at which today's goods and services, real goods, are exchanged for future goods and services. The fact that the market interest rate will be directly influenced by inflationary processes was first suggested by I. Fisher, who determined the nominal interest rate and the expected inflation rate.

The relationship between the rates can be represented by the following expression:

i=r+e, where i is the nominal, or market, interest rate, r is the real interest rate,

e – inflation rate.

Only in special cases, when there is no price increase in the money market (e = 0), do real and nominal interest rates coincide. The equation shows that the nominal interest rate can change due to changes in the real interest rate or due to changes in inflation. Since the borrower and lender do not know what rate inflation will take, they proceed from the expected rate of inflation. The equation becomes:

i=r+e e, Where e e expected inflation rate.

This equation is known as the Fisher effect. Its essence is that the nominal interest rate is determined not by the actual rate of inflation, since it is unknown, but by the expected rate of inflation. The dynamics of the nominal interest rate repeats the movement of the expected inflation rate. It must be emphasized that when forming a market interest rate, it is the expected inflation rate in the future, taking into account the maturity of the debt obligation, that matters, and not the actual inflation rate in the past.

If unexpected inflation occurs, then borrowers benefit at the expense of lenders, since they repay the loan with depreciated money. In the event of deflation, the lender will benefit at the expense of the borrower.

Sometimes a situation may arise where real interest rates on loans are negative. This can happen if the inflation rate exceeds the growth rate of the nominal rate. Negative interest rates can be established during periods of runaway inflation or hyperinflation, as well as during an economic downturn, when demand for credit falls and nominal interest rates fall. Positive real interest rates mean higher income for lenders. This occurs if inflation reduces the real cost of borrowing (credit received).

Interest rates can be fixed or floating.

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

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

FISCHER EQUATION equation of exchange, the main equation of the quantitative theory of money, which forms the basis of modern monetarism, which treats money as the main element of a market economy. According to the Fisher equation, the product of the money supply and the velocity of money circulation is equal to the product of the price level and the volume of the national product:

where M is the amount of money in circulation; V - velocity of money circulation; P - price level; Q - volume (quantity) of goods.

In his book “The Purchasing Power of Money” (1911), Irving Fisher analyzed the effect of changes in the structure of payments in the economy on the velocity of circulation of money. He concluded that price shifts change the demand for money, and therefore the amount of money needed for circulation changes. This interpretation is actively used by modern monetarists when constructing the theory of demand for money.

It is customary to evaluate the interest rate in two projections: nominal and real values.

The essence of the nominal rate

Based on the definition of this concept, it is clear that the nominal interest rate does not take into account changes in price growth and other financial risks. The nominal rate can be taken into account by market participants only as an indicative value.

Mathematical effect of the nominal rate

Real rate + Expected inflation rate = Nominal rate

What matters when setting a market rate is the future rate of inflation, taking into account the maturity of the debt claim, and not the actual rate that was in the past.

Equality between the nominal and real rates is possible only in the complete absence of deflation or inflation. This state of affairs is practically unrealistic and is considered in science only in the form of ideal conditions for the functioning of the capital market.

Nominal compound interest rate

In order to correctly assess the expected income from the use of financial resources over a long period of time, economists advise taking into account the compound interest scheme. When calculating profit using the compound interest method, at the beginning of each new standard period, profit is calculated on the amount received based on the results of the previous period.

Any market mechanism in a changing environment, especially such as the domestic economy, is always associated with high risks. Be it a loan agreement or investing in securities, opening a new business or depository cooperation with a bank. When always assessing potential profit, you need to pay attention to external factors and the real state of the market. Based only on nominal profitability, you can make an incorrect, obviously unprofitable, or even potentially disastrous financial decision.