Nominal and real interest rates. Nominal interest rate What is nominal and real interest rate
Quite often, you can see, at first glance, lucrative offers that promise financial independence. These can be bank deposits and opportunities for investment portfolios. But is everything as profitable as the advertisement says? We will talk about this within the framework of the article, having found 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 reflects nominally the benefit that a particular person can receive when investing in something. It should be noted that there are quite a few opportunities to lose 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 under study. So, the safest are those that offer a rate of return of up to 20%. The high-risk group includes assets that promise up to 70% per annum. And everything that is more than these indicators is a danger zone, into which one should not meddle 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 the nominal rate
Determining the nominal is very simple - it is understood as the value that is given to market assets and evaluates them without taking into account inflation. As an example, we can cite 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. Therefore, they put it in the bank for one year. And at the end of the term, they took 120 thousand rubles. Your net profit is as much as 20,000.
But is it really so? Indeed, during this time, food, clothing, travel could have significantly increased in price - and, say, not by 20, but by 30 or 50 percent. What to do in this case to get a real picture of the case? What should you give preference to when you have a choice? What should be chosen as a benchmark for yourself: the nominal rate and the real rate, or something one of them?
Real rate
For such cases, there is such an indicator as the real rate of return. It is noteworthy that it is quite easy to calculate it. To do this, subtract the expected inflation rate from the nominal rate. Continuing the example given earlier, we can say this: you put 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 we adjust their cost, then 9,000 according to the purchase opportunity of the last year.
This option allows you to get, albeit insignificant, but profit. Now we can consider another situation in which inflation has already reached 50 percent. You don't need to be a genius of mathematics to understand that the state of affairs forces you to look for some other way to save and increase your funds. But so far, all this has been in the style of a 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 take a look at why. For the first time, the idea of the relationship between nominal and real rates and inflation was put forward by the economist Irving Fisher. In the form of a formula, everything looks like this:
NS = RS + OTI
NA is the nominal rate of return;
OTI is the expected inflation rate;
PC 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 the amount at which the real remains unchanged.
It may seem difficult, but now let's figure it out in more detail. The fact is that when the expected is 1%, then the denomination also rises by 1%. Therefore, it is impossible to create a quality investment decision-making process without taking into account the differences between rates. Earlier you just read about the thesis, but now you have mathematical proof that everything described above is not a simple invention, but, alas, a sad reality.
Conclusion
And what can be said in conclusion? Always, if you have a choice, you need to have a high-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 potential losses, always use economic tools. So, the nominal interest rate may promise you a pretty good profit now, but when evaluating all the parameters, it will turn out that not everything is so rosy. And the economic toolkit will help to calculate which decision will be most profitable.
The loan repayment scheme is considered one of the decisive factors at the stage of borrowing funds. Choosing the optimal payment schedule, the borrower gets the opportunity to fully fulfill his obligations to the bank in a timely manner. However, one should not forget about the accrual of interest on the loan. For loans, effective, nominal and real interest rates are usually considered. The pattern of loan repayment is considered one of the decisive factors at the stage of borrowing funds. Choosing the optimal payment schedule, the borrower gets the opportunity to fully fulfill his obligations to the bank in a timely manner. However, one should not forget about the accrual of interest on the loan. For loans, effective, nominal and real interest rates are usually considered.
Nominal interest rate
The lending rate is the percentage of the loaned amount of money that the borrower pays to the lender based on the terms of the contract, so many factors affect the settlement. The nominal interest rate is the simplest metric used to calculate loan payments that are charged on a regular basis (usually annually).
Features of the nominal interest rate:
- Depends on market conditions.
- Calculated excluding inflation.
- Reflects the current loan price.
- Allows you to calculate regular payments.
Thus, the nominal interest rate on the loan is an indicator without adjusting for inflation. The use of such a settlement mechanism means that various currency shocks are not able to affect the selected rate.
In other words, the lending stage does not take into account the fact that the value of money changes over time due to inflation. Since it is impossible in the long term to predict future exchange rates and other factors that significantly affect the credit market, for the participants in the transaction, a fixed rate of return turns out to be safer and more profitable than other schemes for calculating interest payments.
The concept of the real interest rate is applied to account for inflation. It is useful in the case of issuing loans aimed at subsequent growth in interest payments.
The real interest rate measures the change in the cost of the initial cost of the loan, including interest, additionally taking into account inflation, but ignoring any additional payments agreed by the contract.
Effective interest rate
As part of calculating the effective lending rate, the amount of capitalization is taken into account. This indicator allows you to determine the full cost of the loan.
Borrowers can use the obtained data to select the most advantageous offers from commercial banks and other organizations operating in the modern credit market. To determine the effective interest rate, you should study the provided contract. The list of additional services provided by the credit institution is of key importance.
Distinctive features of an effective lending rate:
- Has informational value when choosing a loan product.
- Consists of the nominal rate and the capitalization amount.
- Allows you to determine the full cost of a specific loan.
- Used by the Central Bank to calculate market averages The total cost of the loan is an informational indicator that allows you to determine the actual amount of interest and other payments paid by the client for the use of borrowed funds. "> UCS.
- Depends on the specific conditions of the contract signed by the parties.
The effective rate is often higher than the amount of annual interest accrued on the loan due to taking into account the effect Compounding (from the English compaund - connection) - the process of increasing the initial amount of money as a result of interest. "> compounding... When it comes to borrowing money, the client of the lending institution will pay more in the long run as the initial loan amount increases after interest has been charged. The calculation of the effective rate will make it possible to clarify the terms of lending. The borrower will be able to select the best offers for the transaction, taking into account minor factors affecting the UCI indicator.
How does the effective rate differ from the nominal rate?
The main distinguishing feature of the nominal rate is the simplicity of the calculation. We are talking exclusively about the amount of remuneration that the borrower is obliged to provide to the lender in accordance with the agreement. Any external factors and additional parameters of the transaction are not taken into account. If it is necessary to calculate the level of loan payments taking into account inflation, it is recommended to use the real rate. In turn, adding the amount of capitalization to the nominal indicators, the potential borrower will receive data on the effective rate, which is equal to the full value of the loan agreement under consideration.
Both effective and nominal interest rates can be used to determine the interest on a loan throughout the year. If interest is calculated on an annual basis, then the current and nominal rates will be absolutely identical. However, using any other time period for calculating interest changes the payment parameters. As a result, effective rates can be easily compared, but several nominal indicators have to be adjusted until the total percentage interval is obtained.
Percentage is absolute value. For example, if 20,000 is borrowed, and the debtor has to repay 21,000, then the percentage is 21,000 - 20,000 = 1,000.
The rate (norm) of the loan interest - the price for using money - is a certain percentage of the amount of money. It is determined at the point of equilibrium between supply and demand of money.
Very often in business practice, for convenience, when they talk about lending interest, they mean the interest rate.
Distinguish between nominal and real interest rates. When people talk about interest rates, they mean real interest rates. However, real rates cannot be directly observed. By concluding a loan agreement, we receive information about the nominal interest rates.
Nominal rate (i)- quantitative expression of the interest rate, taking into account the current prices. The rate at which the loan is issued. The nominal rate is always greater than zero (except for the free loan).
Nominal interest rate is a percentage in monetary terms. For example, if on an annual loan of 10,000 monetary units, 1200 monetary units are paid out. as a percentage, the nominal interest rate will be 12% per annum. Having received an income of 1200 monetary units on the loan, will the lender become richer? This will depend on how prices have changed over the course of the year. If the annual inflation was 8%, then in reality the creditor's income 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 in an increase in the purchasing power of an investor or lender, or the exchange rate at which today's goods and services, real goods, are exchanged for future goods and services. That the market rate of interest would be directly influenced by inflationary processes was first suggested by I. Fisher, which determined the nominal interest rate and the expected inflation rate.
The relationship between 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), 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 of inflation will take, they proceed from the expected rate of inflation. The equation takes the form:
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 inflation rate, since it is not known, but by the expected inflation rate. The dynamics of the nominal interest rate repeats the movement of the expected inflation rate. It should be emphasized that when forming the 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 unforeseen inflation occurs, then borrowers benefit from lenders, as 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 when 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 galloping inflation or hyperinflation, as well as during periods of economic downturn, when demand for loans falls and nominal interest rates fall. Positive real interest rates mean an increase in the income of lenders. This happens if inflation reduces the real cost of the loan (received loan).
Interest rates can be fixed and floating.
Fixed interest rate is established for the entire period of use of borrowed funds without a unilateral right to revise it.
Floating interest rate is the rate on medium and long-term loans, which consists of two parts: a movable basis, which changes in accordance with the market conjuncture and a fixed amount, usually unchanged throughout the entire period of lending or circulation of debt
Financial institutions are trying to attract the attention of clients 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 a super generous offer. However, everyone sees the interest rate figures in large, bright print, and few people read the small print 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 gets. Let's take a closer look at what the nominal and real interest rates are, how they differ, what are their similarities and how to calculate the 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 term established by the agreement. This is what banks indicate when attracting customers to place deposits. It does not reflect the real income of the depositor, 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.
- The expected rate of inflation.
- Other expenses of the depositor, including personal income tax for the difference in excess of the rate from the refinancing rate, increased by 5 pp), etc.
Of all the components, the greatest fluctuations are shown by the annual inflation rate. Its expected value depends on historical fluctuations. If inflation stably shows low values (0.1-1%, as in the West or the USA), then in future periods it is set at about the same level. If the state experienced high inflation rates (for example, in the 90s in Russia this figure reached 2500%), then the bankers are setting 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 on his own or rely on the honest attitude of the bank towards himself.
The real income from investing money on a deposit is always less than nominal, since it takes into account the amount that will turn out taking into account the inflation rate adjustment. The real rate reflects the purchasing power of money at the end of the term of the deposit (i.e. more or less goods can be purchased for the total amount compared to the original).
Unlike the nominal interest, the real one can also have negative values. The client not only will not save his savings, but will also receive a loss. Developed countries deliberately keep real rates negative in order to stimulate economic development. In Russia, real rates are changing from positive to negative, especially recently.
How to calculate the real interest rate on a deposit?
To start calculating, you need to determine all the expenses of the depositor. These include:
- Tax. For deposits, there is a tax on income of individuals of 13%. It is applied if the nominal interest on ruble deposits is 5 pp higher than the SR. (until 31.12.2015, the conditions are in effect that personal income tax will be taxed 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 grows, so does the price of goods and services. As of May 2015, inflation was estimated at 16.5%. At the end of the year, its projected value is estimated at 12.5% (taking into account the stabilization of the economic situation).
Let's look at example 1.
The depositor 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 (ND) will be:
100,000+ (100,000 * 20%) = 120,000 rubles.
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 increased his well-being in fact by only 4,772 rubles, and not by 20,000 rubles, as was announced by the bank.
Let's look at example 2.
The depositor 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 rubles.
Tax = 0, because interest rate below CP + 5 p.p.
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 = 2,437.5 rubles.
Thus, in these conditions, the purchasing power of the depositor's savings turned out to be negative. He not only failed to increase his savings, but also lost a part.
Inflationary processes devalue investments, therefore decisions on the loan capital market are made taking into account not only the nominal, but also the real interest rate. Nominal interest rate - this is the current market rate, excluding inflation. Real interest rate - it is the nominal rate minus the expected (implied) inflation rate. The distinction between nominal and real interest rates only makes sense under conditions inflation(increase in the general price level) or deflation(lowering the general price level).
The American economist Irving Fisher put forward a hypothesis regarding the relationship between the nominal and real rates. She got the name Fisher effect , which means the following: the nominal interest rate is changed so that the real rate remains unchanged: i = r + π e ,
where i- nominal interest rate, r- real interest rate, π e - expected inflation rate in percent.
The distinction between nominal and real interest rates is important for understanding how contracts are made in an economy with an unstable general price level. Thus, it is impossible to understand the process of making investment decisions, ignoring the difference between nominal and real interest rates.
6. Discounting and making investment decisions
Fixed capital is a durable production factor, in this regard, the time factor acquires special importance in the functioning of the fixed capital market. From an economic point of view, the same amounts with different time locations differ in size.
What does it mean to get $ 100 in 1 year? This (at a market rate of, for example, 10%) is equivalent to putting $ 91 in a bank for a time deposit today. For a year, interest would have "run up" on this amount, and then in a year it would be possible to receive $ 100. In other words, the current value of the future (received after 1 year) $ 100 is equal to $ 91. Under the same conditions, $ 100 received after 2 years is now worth $ 83.
The discounting method developed by economists makes it possible to compare the sums of money received at different times. Discounting is a special technique for comparing the current (today's) and future value of monetary amounts.
The future value of today's amount of money is calculated using the formula:
where t - number of years, r - interest rate.
Today's value of the future amount of money ( present present value) is calculated by the formula:
Example.
Let's say if you attach today 5 million dollars in fixed assets, then you can build a plant for the production of household utensils, and within future 5 years to receive annually 1200 thousand dollars. Is this a profitable investment project? (in 5 years, will $ 6 million be received, will the profit be $ 1 million?)
Let's calculate two options. The interest rate on risk-free assets, for example, in the first case is 2%. We use it as discount rates, or discount rates. In the second option, the risk-adjusted discount rate is 4%.
At a discount rate of 2%, the present present value is $ 5,434 million:
at a discount rate of 4%, it is $ 4.932 million.
Next, you need to compare two quantities: the amount of investment (WITH) and the amount of the present present value (PV), those. define net present value (NPV). It is the difference between the discounted amount of expected returns and investment costs: NPV = PV- WITH.
Investing only makes sense when, when NPV > 0. In our example, the net present value at a rate of 2% will be: 5.434 million - 5 million = 0.434 million dollars, and at a rate of 4% - negative value: 4.932 - 5 = -0.068 million dollars. Under such conditions, the criterion of net present value shows the inexpediency of the project.
Thus, the discounting procedure helps business entities to make rational economic choices.
