Calculating the Rate of Inflation

The rate of inflation measures how quickly the general level of prices for goods and services is rising. It tells us the percentage increase in prices over a specific period. A common way to measure inflation is by using a price index, such as the Consumer Price Index (CPI) or Wholesale Price Index (WPI).

When we are given price indices for two different time periods, say \(A_1\) for time 1 and \(A_2\) for time 2, we can calculate the rate of inflation between these two periods. The formula for calculating the rate of inflation is similar to calculating the percentage change in any value over time.

Let \(A_1\) be the price index at the beginning of the period (Time 1).

Let \(A_2\) be the price index at the end of the period (Time 2).

The change in the price index during the period is \(A_2 - A_1\).

To find the percentage change (which is the rate of inflation), we divide the change by the initial value (\(A_1\)) and multiply by 100.

Therefore, the formula for the rate of inflation is:

Rate of Inflation \( = \frac{\text{Change in Price Index}}{\text{Initial Price Index}} \times 100 \)

Rate of Inflation \( = \frac{A_2 - A_1}{A_1} \times 100 \)

Let's look at the given options and compare them to our formula:

• Option 1: \(\frac{A_1}{A_2 + A_1} \times 100\) - This formula does not represent the standard percentage change calculation.
• Option 2: \(\frac{A_2 + A_1}{ A_1} \times 100\) - This calculates something different, not the rate of inflation.
• Option 3: \(\frac{A_1}{A_2 - A_1} \times 100\) - This formula is also not correct for calculating the percentage change or inflation rate.
• Option 4: \(\frac{A_2 - A_1}{ A_1} \times 100\) - This formula correctly represents the percentage change in the price index from \(A_1\) to \(A_2\), which is the definition of the rate of inflation between these two points in time.

Thus, the correct formula for the rate of inflation using price indices \(A_1\) and \(A_2\) is \(\frac{A_2 - A_1}{ A_1} \times 100\).