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Chapter 20: Problem 9

Suppose that the only good you purchase is premium bottled water and that at the beginning of the year, the price of a bottle is \(\$ 2.00\). Suppose you lend \(\$ 1,000\) for one year at an interest rate of 5 percent. At the end of the year, the price of premium bottled water has risen to \(\$ 2.08\). What is the real rate of interest you earned on your loan?

Short Answer

Expert verified
The real rate of interest you earned on your loan is 1%.

Step by step solution

01

Identify the given variables

The initial price of bottled water, denoted as \( P1 \), is \(\$2.00\) while the final price, denoted \( P2 \), is \(\$2.08\). The nominal interest rate, denoted \( r \), is given as 5 percent or 0.05 in decimal form.
02

Calculate the Inflation Rate

The inflation rate can be calculated by subtracting the initial price from the final price, dividing the result by the initial price, and then multiplying by 100. This can be represented as \( \frac{P2 - P1}{P1} × 100\% \). Using the provided values, the inflation rate (\( r_I \)) is therefore \( \frac{2.08 - 2.00}{2.00} × 100\% = 4\% \). The inflation rate is 4%.
03

Calculate the Real Interest Rate

The real interest rate can be calculated by subtracting the inflation rate from the nominal interest rate. This can be represented as \( r - r_I \). Using the calculated and given values, the real interest rate is therefore \( 0.05 - 0.04 = 0.01 \) or 1%.

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Most popular questions from this chapter

(Related to the Apply the Concept on page 688 ) During the late nineteenth century in the United States, many farmers borrowed heavily to buy land. During most of the period between 1870 and the mid-1890s, the United States experienced mild deflation: The price level declined each year. Many farmers engaged in political protests during these years, and deflation was often a subject of their protests. Explain why farmers would have felt burdened by deflation.

Which is a greater problem: anticipated inflation or unanticipated inflation? Briefly explain.

An article in the Wall Street Journal noted that over a fourmonth period in late 2014 , employment in the state of Georgia "rose \(1 \%\) even as the state's jobless rate climbed 1.2 percentage points." Briefly explain how the state's unemployment rate could have increased at the same time that employment in the state was increasing.

What is the natural rate of unemployment? What is the relationship between the natural rate of unemployment and full employment?

In discussing the labor market during the recovery from the \(2007-\) 2009 recession, Federal Reserve Chair Janet Yellen noted that "the employment-to- population ratio has increased far less over the past several years than the unemployment rate alone would indicate, based on past experience." a. During an economic expansion, why would we normally expect the employment- population ratio to increase as the unemployment rate falls? b. Why didn't the employment-population ratio increase as much as might have been expected during the recovery from the \(2007-2009\) recession?
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