# Effective vs. Real Interest Rates: Inflation

A previous post explained the difference between nominal and effective interest rates.  To confuse matters further, there is another important term to understand — real interest rates:

Real interest rates (also known as the real rate of return that a lender receives on a loan) reflect the actual purchasing power of the future balance, and consequently must be adjusted for inflation or deflation.

These three videos from the Khan Academy explain how inflation can reduce the purchasing power of money, and how to adjust for this fact in reporting interest rates. Notice how Salman Khan uses the words “nominal” and “real”, rather than “effective” and “real”, which sort of glosses over previous videos that make an important distinction between nominal and effective interest rates.

To simplify the terminology, here’s a summary:

The difference between nominal and effective interest rates is the compounding period.

The difference between effective and real interests rates is inflation.

Notice that if we simply take nominal = effective (e.g., annual compounding), then the difference between nominal and real is still inflation. Khan’s use of the word “nominal” in these videos makes this simplification.

The difference between effective and real interest rate is often estimated as:

real = effective – inflation

For example, a treasury bond that earns a 2% effective interest rate in an economy with an inflation rate of 1.5% is estimated to be earning a 0.5% real rate of return.

When interest rates are low, and time horizons are only a few years, this approximation is pretty good.  However, it is inexact.

The exact formula is this:

real = ( 1 + effective) / ( 1 + inflation) – 1

In the case of the 2% bond above, the exact real rate of return is actually 1.02/1.015 – 1 = 0.49261% .

Notice that the difference is small!  BUT a high interest rate, high inflation context, the difference becomes very important.  Suppose the effective rate on an investment is 22%, but inflation is running at 18%.  We might estimate the real rate of return as 4%, but the exact real rate of return is 1.22/1.18 -1 or only 3.39% !

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