Final answer:
The annual inflation rate between June 30, 1982, and June 30, 2005, can be calculated by finding the total percentage change in the CPI and then converting it to an annual rate over 23 years. The correct option for the annual inflation rate is b. 4.2805% pa
Step-by-step explanation:
To calculate the annual inflation rate between two dates using the consumer price index (CPI), you must first determine the overall percentage increase in the CPI, and then convert this into an annual rate. The formula to calculate the general percentage change in CPI between two years is given by:
Percentage change = (CPI in later year - CPI in base year) / CPI in base year
Using the provided CPI values, we get:
Percentage Change = (82.6 - 31.5) / 31.5 = 1.6238 or 162.38%
Next, we need to find the annual rate of inflation over the period in question. Since the period spans from 1982 to 2005, there are 23 years in total. The formula to convert the total percentage change to an annual rate is:
Annual Inflation Rate = (1 + Total Percentage Change)^(1/Number of Years) - 1
Applying the formula:
Annual Inflation Rate = (1 + 1.6238)^(1/23) - 1 ≈ 0.0428 or 4.2805%
Therefore, the correct option for the annual inflation rate is b. 4.2805% pa.