# Real interest rate

In economics, the real interest rate denotes the interest rate that indicates the change in the value of an asset , taking into account inflation or deflation . It therefore takes into account that a financial asset loses value or purchasing power when the price level rises or, conversely, gains in value when the price level falls.

The real interest rate is calculated approximately as the difference between the nominal interest rate and the inflation rate. It has an influence on the saving behavior of households, the investment behavior of companies and the financing of the state budget.

## Further definition

The real interest rate is usually understood as the interest rate minus the expected inflation rate; To clarify, one speaks of the expected or ex ante real interest rate. Occasionally, the real interest rate is also understood as an ex post quantity and is calculated using the past inflation rate. Economic decisions depend on the expected real interest rate, asset developments on the actual real interest rate.

## classification

In times of stable prices, i. H. with inflation of zero, the nominal and real interest rates are the same as defined above. However, the nominal interest rate often rises with an increase in the price level (not necessarily by the same percentage that the prices increase). If the inflation rate is higher than the nominal interest rate, this results in a negative real interest rate. In this case, the creditor of a money credit transaction loses capital. The following symbols are used for the mathematical derivation:

• ${\ displaystyle r:}$ Real interest rate
• ${\ displaystyle i:}$ Nominal interest
• ${\ displaystyle \ pi:}$ inflation rate

A fortune grows according to the compounding factor . The exact relationship between nominal interest and real interest is therefore . In the case of small values, the last summand is often neglected because it is of the second order, and the approximation formula is obtained ${\ displaystyle (1 + i) = (1 + r) (1+ \ pi)}$${\ displaystyle i = r + \ pi + r \ pi}$

${\ displaystyle r \ approx i- \ pi}$ .

The Fisher Effect states, under the assumptions of perfect foresight, a perfect market, perfect market transparency and no transaction costs , that the increase in the nominal interest rate i is accompanied by a proportional increase in the inflation rate. The assumptions made cannot be fully met in practice. For this reason, a complete proportionality cannot be assumed in practice . However, a certain temporal relationship between the change in the inflation rate and the change in the nominal interest rate (see Fig. 1) can be demonstrated. ${\ displaystyle \ pi}$

As the rate of inflation increases, so does the current yield on fixed income securities (the current yield on fixed income securities is often used as a measure of the nominal interest rate and denotes the average return on all outstanding fixed income securities in circulation ).

If one looks at the international factor movements within foreign trade theory , the term real interest rate is also used. The real interest rate depends on the preferences for present and future consumption of the individual economies. When a country takes out a loan, it can initially consume more than it produces. This situation is reversed when the loan is repaid. It can consume less than is produced, since part of the production is used for loan repayment and is therefore not available for consumption. Future consumption is more expensive than current consumption by the real interest rate “r”. The level of the real interest rate "r" is determined by the relative world supply and the relative world demand for future consumption.

The real interest rate continues to play a major role in monetary policy . The European Central Bank is responsible for monetary policy in the euro area , whose primary goal is to guarantee price stability and thus to maintain the purchasing power of the euro. By definition, price stability is given by an “increase in the HICP of less than 2%”. If the money supply is too high compared to the supply of goods and services, for example, the general price level rises (inflation) and purchasing power falls. To counteract this, the ECB can pursue a restrictive monetary policy in order to reduce the money supply. Due to its inertia, the inflation rate falls with a time delay, so that it is possible to influence the short-term real interest rate.

The financial policy is better suited to influence the long-term real interest rates as a monetary policy and acts directly on supply and demand in the capital market.

## application

Due to a nominal interest rate (in percent), an asset, for example a savings balance from the bank's interest credit or a property from the market price development , experiences a nominal increase in value over a certain period of time with the factor: ${\ displaystyle i}$

${\ displaystyle 1 + {\ frac {i} {100}}}$

With an inflation rate (in percent), however, at the same time inflation gnaws at the value of the currency and compresses the value of the asset with the factor: ${\ displaystyle \ pi}$

${\ displaystyle {\ frac {1} {1 + {\ frac {\ pi} {100}}}}}$

The real interest rate r (in percent) in the period under review is therefore:

${\ displaystyle r = \ left ({\ frac {1 + {\ frac {i} {100}}} {1 + {\ frac {\ pi} {100}}}} - 1 \ right) \ cdot 100}$

If, then , the real interest rate is 0%. ${\ displaystyle i = \ pi}$

For there is a positive real interest rate, that is, despite the inflationary effect, there is a real increase in the value of the asset. ${\ displaystyle i> \ pi}$

For although a nominal value increase is on paper, in real terms, the value of the asset has, however, reduced. ${\ displaystyle i <\ pi}$

## example

If the nominal interest rate i for a loan is 6% in a certain period and the inflation rate for the same period is 2%, the following result is obtained using the above formula: ${\ displaystyle \ pi}$

${\ displaystyle r = \ left ({\ frac {1 + {\ frac {6} {100}}} {1 + {\ frac {2} {100}}}} - 1 \ right) \ cdot 100 = 3 {,} 92157}$

The lender only has 3.92% real interest of the 6% nominal interest, taking into account inflation of 2%.

According to the interests of the asset owner, the real performance can also vary individually. Because the inflation rate is determined on the basis of an examination of the price development of many products. If a certain entrepreneur wants to finance a certain individual product or a certain mix of goods and services with his investments or by selling a property, the price development of which was more favorable than the general inflation rate, then the real value of the property he is looking at has increased even more than in the above formula. The opposite case is also possible: the prices for the individually planned investments increase more strongly than the generally determined price average. ${\ displaystyle \ pi}$

This also applies to assets that are intended for private consumption. Because often the individual wishes will deviate more or less strongly from the range of products and services for which the general price development was determined and announced in the form of the inflation rate.

If you want to know exactly how the value of your own assets will develop in relation to your personal needs structure, it can be useful to determine an individual inflation rate by keeping a budget book or by observing the price of the products you want to buy. However, it should not be overlooked that the price sometimes also changes the quality of products.

## literature

• Paul R. Krugman, Maurice Obstfeld: International Economy: Theory and Politics of Foreign Trade. 7th edition. Pearson Studies, 2006, ISBN 3-8273-7199-6 .
• The monetary policy of the ECB 2004. European Central Bank, 2004, ISBN 92-9181-491-1 .