Rate of inflation is equal to : [A = Price Index]

Question

Accepted Answer

Explanation:

1. **Correct Answer: Option 4 - $\frac{A_2 - A_1}{A_1} \times 100$**

The rate of inflation is typically calculated as the percentage change in the price index over a specific period. In this context, $A_1$ represents the initial price index, and $A_2$ represents the price index at a later time. The formula for calculating the rate of inflation is:

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

This can be expressed as:

$$
   \frac{A_2 - A_1}{A_1} \times 100
   $$

This formula calculates the percentage increase in the price index from $A_1$ to $A_2$, which is the standard method for determining the rate of inflation. Therefore, Option 4 is correct.

2. **Explanation of Incorrect Options:**

- **Option 1: $\frac{A_1}{A_2 + A_1} \times 100$**

This formula does not represent the rate of inflation. It attempts to calculate a ratio of the initial price index to the sum of the initial and final price indices, which does not provide any meaningful measure of inflation. Inflation is concerned with the change in price levels, not their sum.

- **Option 2: $\frac{A_2 + A_1}{A_1} \times 100$**

This formula calculates a ratio that includes both the initial and final price indices in the numerator, which is not relevant for determining the rate of inflation. The rate of inflation should focus on the change (difference) between the two indices, not their sum.

- **Option 3: $\frac{A_1}{A_2 - A_1} \times 100$**

This formula incorrectly places the initial price index in the numerator and the change in price index in the denominator. This does not align with the standard calculation for inflation, which requires the change in price index to be in the numerator to express the percentage change relative to the initial index.

In conclusion, Option 4 correctly represents the formula for calculating the rate of inflation as it measures the percentage change in the price index from an initial value to a final value. The other options do not accurately capture this concept and are therefore incorrect.