# Real Interest

Real interest differs from nominal interest in that it accounts for inflation or deflation, or changes in purchasing power.

In other words, real interest describes the volume of goods or services which the interest earned or paid can purchase. When real interest is low or negative, the purchasing power of that interest at the time it is paid or charged is low or negative.

The term is often used synonymously with “real interest rate”. However, real interest rates are shown as percentages (2%, for example) while real interest is shown as a whole number (CHF 20, for example).

Real interest (r) is relatively easy to calculate based on nominal interest (i) and an inflation rate (π).

Here is the formula:
(1 + r) = (1 + i) / (1 + π).

In reverse, the formula works like this:
r = (i – π) / (1 + π) or
r = ((1 + i) / (1 + π)) – 1.

Here is an approximate – but not completely accurate – formula for finding real interest:
r ≈ i – π.

Example: A free savings account has an interest rate of 3% per annum. A person who deposits CHF 1000 in that account will have a total of CHF 1030 in their account after 1 year. In this case, the nominal interest earned is CHF 30.

However, if an inflation rate of 2% per annum applied to the same year, the real interest would be much lower at (0.03-0.02) / (1+0.02) = 0.01 / 1.02 ≈ 0.009804 (0.9804%). So each CHF 1 of nominal interest would only be worth CHF 0.98 (1 / 1.02) ≈ CHF 0.98.

Important: Simply subtracting the inflation rate from the nominal interest rate does not provide an accurate calculation of real interest. In the above example, the real interest rate is not quite 1% but approximately 0.98%.

An inflation rate of 2% indicates a 2% increase in prices. This does not equal a 2% decrease in your money’s purchasing power, but a 1.96% decrease in your money’s purchasing power (1 / 1.02 ≈ 0.9804 and 1 – 0.9804 = 0.0196 = 1.96%). In this case, after one year CHF 1030 will buy the same amount of goods and services that you could buy with CHF 1009.80 the previous year.

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