Real Interest Rate Formula

• The nominal rate of interest is mostly quoted by the banks or any other financial institutions. Hence, the first-rate that is used in the calculation is the nominal rate of interest.
• The second one is the inflation rate which can be the actual rate of interest or it could be an expected rate of interest.
• The difference between the two that is a nominal rate of interest and inflation rate will be a real rate of interest.

Examples

Example #1

The nominal rate of interest that has been prevailing for a long time has been around 9% and the rate of inflation has been come out as 3%. You are required to calculate the real rate of interest.

Solution:

Use below given data for calculation of real interest rate.

Calculation of real interest rate can be done as follows:

We are given both figures to calculate the real rate of interest.

Real Interest Rate = 9% – 3%

Real Interest Rate will be –

Real Interest Rate = 6%

Hence, the real rate of interest is 6%.

Example #2

World bank has been in task of completing statistics figures of some of the countries. They are now left with two countries for which the deadline to complete the statistics is by next week. William has joined the team recently which does the calculation of interest rates. William is an economist and has done the master’s in it. He was given a task to complete calculation of the real rate of interest for the remaining two countries X and Y. Below are the details that were collected by the ex-employee for these countries.

Based on the above available information, you are required to calculate the real rate of interest. If someone wants to invest their funds, where should one invest whether in Country X or Country Y?

Here, we have to have a nominal rate of interest which is the deposit rate of interest, but we are not given the real rate of interest which we shall calculate for both countries.

Inflation Rate for Country X will be –

Inflation Rate = 123,331,456.43 / 120,899,345.98 – 1 = 2.01%.

Calculation of Real Interest Rate for Country X can be done as follows:

Real Interest Rate = 11% – 2.01%

Real Interest Rate for Country X will be –

Real Interest Rate = 8.99%

Inflation Rate for Country Y will be –

Inflation Rate = 141,678,331.23 / 140,993,221.77 – 1 = 0.49%

Calculation of Real Interest Rate for Country Y can be done as follows:

Real Interest Rate = 10.50% – 0.49%

Real Interest Rate for Country Y will be –

Real Interest Rate = 10.01%

Hence, in real terms, it is better to invest in country Y as the country provides a higher rate of interest.

Example #3

XYZ wants to invest in a fixed deposit, and he wants ABC bank. The bank pays a 7% rate of interest irrespective of the duration and amount. The fixed deposit amount is $100,000. He happily invests the amount for a period of 3 years. Later, on a news channel, he learns that the country is facing a high level of inflation and currently its 8% and further it was expected that after 3 years it will be 8.50%.

Based on the above scenario, you are required to confirm whether XYZ will earn or lose money?

Solution:

Use below given data for calculation of real interest rate.

First, we shall calculate the real rate of interest. Since XYZ is investing for 3 years, and hence while calculating a real rate of interest, we shall use the expected inflation rate of interest which is 8.50% and not 8.00%.

Calculation of real interest rate can be done as follows:

Real Interest Rate = 7% – 8.50%

Real Interest Rate will be –

Real Interest Rate = -1.50%

Hence, the real rate of interest is -1.50%, which clearly indicates XYZ will lose money in real terms since inflation is greater than the rate of interest offered by the bank.

Relevance and Uses

• The real rate of interest shall adjust the observed interest rate of the market so as to remove the effects of ongoing or expected inflation.
• The real rate of interest does reflect the purchasing power value of the interest which is paid on a loan or an investment and which shall represent the rate of interest that will be preferred time of the lender and the borrower.
• As the rate of inflation does not remain constant, the prospective real rate of interest will rely on the estimates of future inflation that will be expected over the time to maturity of an investment or a loan.
•  The conclusion is that an investor earns a real rate and not a nominal rate as the other part of the nominal rate is eaten by inflation.

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