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INFLATION AND INTEREST RATES

Whenever anyone quotes an interest rate, you can be fairly sure that it is a nominal, not a real rate. It sets the actual number of dollars you will be paid with no offset for future inflation.

If you deposit $1,000 in the bank at a nominal interest rate of 6 percent, you will have $1,060 at the end of the year. But this does not mean you are 6 percent better off. Suppose that the inflation rate during the year is also 6 percent. Then the goods that cost $1,000 last year will now cost $1,000 1.06 = $1,060, so you`ve gained nothing:

Real future value of investment = $1,000 (1 + nominal interest rate) (1 + inflation rate) = $1,000 1.06 = $1,000 1.06

In this example, the nominal rate of interest is 6 percent, but the real interest rate is zero.

The real rate of interest is calculated by

1 + real interest rate = 1 + nominal interest rate 1 + inflation rate

In our example both the nominal interest rate and the inflation rate were 6 percent. So

1 + real interest rate = 1.06 = 1 1.06 real interest rate = 0

What if the nominal interest rate is 6 percent but the inflation rate is only 2 percent? In that case the real interest rate is 1.06/1.02 Ј 1 = .039, or 3.9 percent. Imagine that the price of a loaf of bread is $1, so that $1,000 would buy 1,000 loaves today. If you invest that $1,000 at a nominal interest rate of 6 percent, you will have $1,060 at the end of the year. However, if the price of loaves has risen in the meantime to $1.02, then your money will buy you only 1,060/1.02 = 1,039 loaves. The real rate of interest is 3.9 percent.

NOMINAL INTEREST

RATE Rate at which money invested grows.

REAL INTEREST RATE

Rate at which the purchasing power of an investment increases.

Here is a useful approximation. The real rate approximately equals the difference between the nominal rate and the inflation rate:6

Real interest rate вЙИ nominal interest rate Ј inflation rate

Our example used a nominal interest rate of 6 percent, an inflation rate of 2 percent, and a real rate of 3.9 percent. If we round to 4 percent, the approximation gives the same answer:

Real interest rate вЙИ nominal interest rate Ј inflation rate вЙИ 6 Ј 2 = 4%

The approximation works best when both the inflation rate and the real rate are small.7 When they are not small, throw the approximation away and do it right.

Real and Nominal Rates

In the United States in 1999, the interest rate on 1-year government borrowing was about 5.0 percent. The inflation rate was 2.2 percent. Therefore, the real rate can be found by computing

1 + real interest rate = 1 + nominal interest rate 1 + inflation rate = 1.050 = 1.027 1.022 real interest rate = .027, or 2.7%

The approximation rule gives a similar value of 5.0 Ј 2.2 = 2.8 percent. But the approximation would not have worked in the German hyperinflation of 1922 Ј1923, when the inflation rate was well over 100 percent per month (at one point you needed 1 million marks to mail a letter), or in Peru in 1990, when prices increased by nearly 7,500 percent.

6 The squiggle (вЙИ) means ¬approximately equal to. ­ 7 When the interest and inflation rates are expressed as decimals (rather than percentages), the approximation error equals the product (real interest rate inflation rate).