The real interest rate is equal to the nominal interest rate. Real interest rate

The Nominal Interest Rate is the market interest rate, excluding inflation, that reflects the current valuation of monetary assets.

The Real interest rate is the nominal interest rate minus the expected inflation rate.

For example, the nominal interest rate is 10% per annum and the projected inflation rate is 8% per annum. Then the real interest rate will be: 10 - 8 = 2%.

Nominal and real inflation rate

The difference between the nominal rate and the real rate makes sense only in conditions of inflation or deflation. American economist Irving Fisher suggested a connection between the nominal and real interest rates and inflation, called the Fisher effect, which states: the nominal interest rate changes by the amount at which the real interest rate remains unchanged.

In formula form, the Fisher effect looks like this:

i = r + πe

where i is the nominal interest rate;
r is the real interest rate;
πe is the expected inflation rate.

For example, if the expected inflation rate is 1% per year, the nominal rate will increase by 1% for the same year, therefore, the real interest rate will remain unchanged. Therefore, it is impossible to understand the investment decision-making process of economic agents without taking into account the difference between the nominal and real interest rates.

Let's take a simple example: let's say you intend to give someone a loan for one year in an inflationary environment, what exact interest rate will you set? If the growth rate of the general price level is 10% per year, then by setting the nominal rate at 10% per annum for a loan of 1000 rubles, you will receive 1100 rubles in a year. But their real purchasing power will no longer be the same as it was a year ago.

Nominal increase in income amounting to CU 100. will be “eaten up” by 10% inflation. Thus, the distinction between the nominal interest rate and the real interest rate is important for understanding how exactly contracts are concluded in an economy with an unstable general price level (inflation and deflation).

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.

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.

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

The term "interest rate" is one of the most commonly used phrases in the consumer finance and fixed income investing industry. Of course, there are several types of interest rates: real, nominal, effective, annual, etc.

The differences between different types of rates, such as nominal and real, are based on several key economic factors. But while these technical variables may seem trivial, lending institutions and retailers have taken advantage of the public's general ignorance of these differences to rake in hundreds of billions of dollars over the years. Thus, those who understand the difference between nominal and real interest rates have taken an important step toward becoming smarter consumers and investors.

Nominal interest rate

The nominal interest rate is conceptually the simplest type of interest rate. It is simply the stated interest rate on a given bond or loan. This type of interest rate is called a fixed income investment coupon rate because it is the issuer-guaranteed interest rate that was traditionally printed on the coupons that were redeemed by bondholders.

The nominal interest rate is essentially the actual money price that borrowers pay lenders for using their money. If the nominal loan rate is 5%, then borrowers can expect to pay $5 for every $100 they lend.

Real interest rate

The real interest rate is a little more complicated than the nominal rate, but is still fairly simple. The nominal interest rate does not tell the whole story because inflation reduces the purchasing power of the lender or investor so that they cannot buy the same amount of goods or services at payment or maturity with a certain amount of money as they can now.

The real interest rate is so named because it states the “real” rate that a lender or investor receives after inflation; that is, an interest rate that exceeds the rate of inflation. If a compounding bond has a nominal yield of 6% and the inflation rate is 4%, the real interest rate is only 2%.

The real interest rate can be considered the actual mathematical rate at which investors and lenders increase their purchasing power through their bonds and loans. It is possible that real interest rates will be negative if the inflation rate exceeds the nominal investment rate. For example, a bond with a nominal rate of 3% will have a real interest rate of -1% if the inflation rate is 4%. So the comparison between real and nominal interest rates can be summarized in this equation:

Nominal Interest Rate - Inflation = Real Interest Rate

From this formula several economic terms can be derived that lenders, borrowers and investors can use to make more informed financial decisions.

Real interest rates can not only be positive or negative, but can also be higher or lower than nominal rates. Nominal interest rates will exceed real rates when the inflation rate is a positive number (as it usually is). But real rates can also exceed nominal rates during periods of deflation.

The hypothesis states that the inflation rate moves in tandem with nominal interest rates over time, meaning that real interest rates become stable over longer periods of time. Thus, investors with longer time horizons can more accurately estimate their investment returns on an inflation-adjusted basis.

Effective interest rate

Another type of interest rate that investors and borrowers should be aware of is called the effective rate, which takes into account compliance.

For example, if a bond pays 6% interest and is compounded biannually, then an investor who invests $1,000 in that bond will receive $30 after the first 6 months ($1,000,000) and $30. 90 percent after the next 6 months (1,030 x 03). The investor received a total of $60. 90 for the year, which means that while the nominal rate was 6%, the effective rate was 6.09%.

From a mathematical perspective, the difference between the nominal and effective rates increases with the number of compounding periods within a given period. Please note that the rules regarding how the AER on a financial product is calculated and advertised are less strict than for the annual percentage rate (APR).

Applications

The main benefit of knowing the difference between nominal, real and effective rates is that it allows consumers to make better decisions about their loans and investments.

For example, a loan with frequent prescriptions will be more expensive than one that is collected annually. Keep these differences in mind when shopping for a mortgage.

Understanding interest rates also applies to investing. A bond that pays only 1% in real interest may not be worth investors' time if they are looking to increase their holdings over time. These rates effectively reveal the true return that will be posted on a fixed income investment and the true cost of borrowing for an individual or business.

Investors looking for inflation protection in a fixed-income rental can turn to instruments such as Treasury Inflation-Protected Securities (TIPS), which pay an interest rate indexed to inflation. In addition, mutual funds invest in bonds, mortgages and senior secured loans that pay variable interest rates that are adjusted periodically to current rates.

Bottom line

Interest rates can be broken down into several subcategories that include various factors such as inflation. Smart investors know that they can look beyond the par or coupon rate of a bond or loan to make sure it meets their investment goals. Contact your financial advisor if you need professional advice on interest rates and investments that keep up with inflation.

The interest rate is the relative amount of interest payments on loan capital over 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.

The nominal interest rate is interest in monetary terms. The real interest rate is the 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 relationship between the rates can be represented by the following expression:

where i is the nominal, or market, interest rate;

r - real interest rate;

r - inflation rate.

Only in special cases, when there is no price increase in the money market (p = 0), do real and nominal interest rates coincide. Equation (2) 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:

where r e is the expected inflation rate.

Equation (3) 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 rate of inflation 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. If we compare the actual inflation index with the dynamics of the average rate on short-term loans, we can confirm the existence of a relationship between the nominal interest rate and the level of inflationary depreciation of money. 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. A fixed interest rate is established for the entire period of use of borrowed funds without the unilateral right to revise it. A floating interest rate is a 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. The interest rate system includes rates of the monetary and stock markets: rates on bank loans and deposits, treasury, bank and corporate bonds, interbank market interest rates and many others. Their classification is determined by a number of criteria, including: forms of credit, types of credit institutions, types of investments involving credit, loan terms, types of operations of a credit institution. bank loan interest rate

The main types of interest rates that both lenders and borrowers rely on include: the base bank rate, the money market interest rate, the interest rate on interbank loans; interest rate on Treasury bills.

Let's look at some types of nominal interest rates.

The base bank rate is the minimum rate set by each bank for loans provided. Banks provide loans by adding a certain margin, i.e. a premium to the base rate on most retail loans. The base rate includes the bank's operating and administrative expenses and profit. The rate is set independently by each bank. An increase or decrease in the rate of one bank will cause similar changes in other banks.

Interest rates for commercial, consumer and mortgage loans. This type of rate is well known both to entrepreneurs who take out loans from banks to develop their business, and to individuals. The actual loan rate will be determined as the sum of the base rate and the premium. The premium represents a premium for the risk of default by the borrower, as well as a premium for the risk associated with the maturity of the loan. However, if in commercial lending the interest rate is known to the borrower in advance, then in consumer loans the real effective rate is veiled by various marketing ploys and burdened with additional deductions: for example, with an announced rate of 20% per annum, the real payment turns out to be much higher, sometimes reaching 80-100% per annum .

Rates on time deposits (deposits) of individuals and companies in commercial banks. The overwhelming majority of enterprises, as well as an increasing number of individuals, have accounts in commercial banks, place ruble funds in time deposits (i.e. deposits), receiving interest for this, expressed when concluding a deposit agreement in the form of an interest rate. Deposit rates on passive operations of banks are influenced by the same market processes as rates on active operations. Deposit rates are closely related to other rates in the monetary and stock markets. A legal entity that wants to deposit a certain amount of money can buy bonds on the organized market or promissory notes on the unorganized market. A deposit with a bank is more convenient in terms of registration, but the availability of alternative options for placing funds means that banks cannot lower interest rates on deposits too much.

Rates on debt securities (bonds, certificates of deposit, bills, commercial paper, notes, etc.) refer to capital market interest rates. In debt securities there is an interest rate at which the borrower - the issuer of the security - borrows money. These rates are also very diverse: coupon on multi-year bonds, interest rate on bills and certificates of deposit, yield to maturity. Coupon rates indicate the interest income on the face value of the bonds. Yield to maturity shows interest income taking into account the market value of bonds and reinvestment of the resulting coupon income.

The Treasury bill interest rate is the rate at which Western central banks sell Treasury bills on the open market. Treasury bills are discounted securities, i.e. they are sold below par, so the rate is considered a discount yield.

The interest rate on interbank loans refers to money market interest rates. Many media outlets publish lending rates on the interbank market, when one commercial bank lends to another for a certain period in the form of transactions. These interbank lending rates (IBC) are less known to the general public in contrast to bank rates on private deposits. Such rates are the most flexible and more focused on market conditions.

The reference rate is a necessary infrastructure element of any loan market for transactions with interest-bearing instruments. When making a decision to issue or receive a loan, to invest or save funds, any economic individual (both banks and enterprises and individuals) needs a basic indicator - a generally accepted indicator of the interest rate, which would serve as a guideline for the general level of interest rate in a given currency, with which it would be possible to compare all kinds of rates on various financial instruments and deposit and credit products in the money market. In international practice, the role of a universal guiding light among numerous rates is played by interest rate indices, also called reference rates. For longer periods of lending money (and this is the capital market), the role of a general reference point is played by the rate of return on long-term government bonds.