The real rate of return formula calculates the annual return on an investment that takes inflation into account. Adjusting nominal rate of return to price changes on the market allows evaluating the effective return on the investment.

### How to calculate real rate of return?

For a quick approximate calculation, you can simply subtract the inflation rate from the nominal rate, but for more accurate calculation the following formula is used:

$Real\;Rate\;of\;Return = \frac{ 1 + nominal\;rate }{1 + inflation\;rate} - 1$

Nominal rate is a rate that bank or investment offers.

To find out the inflation rate we can use consumer price index (or other price indexes like GDP deflator).

The inflation rate is calculated as:

$Inflation\space Rate = \frac{CPI_{x} - CPI_{y}}{CPI_{y}} \times 100\%$

Where y is the initial consumer price index for the calculated period/time, and x is the ending consumer price index for the period calculated.

### Example of real rate of return calculation

• An individual decides to make a deposit.
• Bank offers an interest rate of 6% annually.
• The inflation rate is 2%.

What is the real rate of return?

$Real\;Rate\;of\;Return = \frac{ 1 + 6\% }{1 + 2\%} - 1 = 3.92\%$

The real rate of return will be 3,92%. That means that if this individual locates $100,000 into his account, the real value of his money won’t be$106,000, but will be $103,920. However, if he won’t make this deposit and will keep this capital in cash, the real value of his money will be$100,000 × (100%-2%) = \$98,000.

### The difference between the real rate of return and nominal rate

Interest rates can be expressed as nominal rates or as real rates. Real rates of return take inflation into account and nominal rates don’t.

• Inflation.  If there is inflation, the nominal rates will always be higher than real rates.
• Deflation. If there is “a negative inflation” or a deflation, when the general price level decreases, the nominal rate will be lower than the real rate of return.
• If the prices stay on the same level and the inflation rate is 0, then the nominal rate of return is equal to the real rate of return.

### Real rate of return effects

The real rate of return has a positive value only when the nominal rate is higher than the inflation rate. This means that:

• Deposits. In the case of deposits there are reasons to save due to the fact that income from the deposit is higher than the price increase in a given period.
• Loans. The borrower incurs some additional costs for early loan payoff. These costs increase when the prices increase, but the borrower has avoided them by taking out a loan. These costs should cover the price of the bank services.

A negative real rate of return means:

• Free cash. For holders of free cash, lack of willingness to save and a high tendency to buy to avoid losses.
• Loans. For borrowers it means some additional benefits, because taking out a loan allows us to „be in advance” of price increases. This means to save the difference between the new prices and the nominal interest rate on the loan.

### Dependencies between inflation and interest rates

• As the inflation rate increases, real interest rates are decreasing. This happens because high inflation makes savings decrease faster than payments of interest, which are calculated according to the nominal interest rate.
• A lower level of expected inflation increases the cost of raising capital, at a given level of nominal interest rate. As a result, people will borrow less money, and companies will issue fewer bonds, and bond supply will decrease.
• Who loses and who gains? In a situation when the real inflation rate is higher than expected, borrowers gain, and lenders lose. In this situation, borrowers will return the money with a lower real value than expected earlier. If the actual inflation rate is lower than expected, the lenders will gain, and the borrowers will lose. Borrowers will return the money with a higher real value than they expected earlier.