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The cost-of-living index is a crucial economic measure that looks at the change in the price of goods and services over time. It's intended to help gauge how inflation affects the purchasing power of consumers. When the index rises, it indicates that living costs have increased, requiring more money to maintain the same lifestyle.
In our example, the index increased by 3% each year for 6 years. This means the general cost of goods and services rose 3% annually. It's a simple percentage increase so, every year, the cost is compounded by this 3%, making it slightly more expensive over time.
Understanding this concept helps you see why salaries need adjustment. It ensures people can afford the same items they previously could despite price hikes.

Calculating a salary increase involves understanding how compound interest works since salary increments typically work on a compounded basis. In our example, the salary increase is tied directly to the cost-of-living index, plus an additional guaranteed increase of 2%.
So, when the cost-of-living index went up by 3%, the EUW Union ensured that salaries increased by 5% (3% + 2%) each year. This is where the compound interest formula steps in: \[ A = P(1 + r/100)^n \]Here, \( A \) is the final salary, \( P \) is the initial salary, \( r \) is the combined annual salary increase (5%), and \( n \) is the number of years.
Because these increases are compounded annually, it is crucial to apply the formula accurately to find out what the salary would be after a certain period, like 6 years in this problem. This calculation ensures that salary growth is aligned correctly with both inflation and the negotiated union increase.

The EUW Union plays a critical role in ensuring workers' salaries keep pace with the cost of living and beyond. Through negotiations, they secure agreements that consider inflationary trends.
In this exercise, the union negotiated not only a match to the inflation rate reflected in the cost-of-living index but an additional 2% increase annually for their members. This ensures that union members not only maintain but slightly improve their purchasing power over the years. These negotiations reflect the union's role in advocating for fair and sustainable wage practices.
Such agreements are vital, as they protect workers from the eroding effects of inflation, which can decrease the real value of money if not counterbalanced by the same or higher salary increments.