Question

A price index was approximately 97.8 (base year 1992) at the beginning of 1991. If inflation continued at an average annual rate of 3.7%, what would the index be at the beginning of 2023 ?

The index would be__

Answer 1

To find the price index at the beginning of 2023, calculate the cumulative inflation rate from 1991 to 2023 using the given inflation rate of 3.7% per year. Multiply the base year index of 97.8 by the cumulative inflation rate to get the index at the beginning of 2023, which is approximately 128.697.

Step-by-step explanation:

To find the price index at the beginning of 2023, we need to calculate the cumulative inflation rate from 1991 to 2023 and apply it to the base year index. The cumulative inflation rate can be calculated using the formula:

Cumulative inflation rate = ((1 + Inflation rate)^n) - 1

Given that the inflation rate is 3.7% per year, and the number of years is 2023 - 1991 = 32, the cumulative inflation rate is:

Cumulative inflation rate = ((1 + 0.037)^32) - 1 = 1.315 - 1 = 0.315

Multiplying the base year index of 97.8 by the cumulative inflation rate gives us the index at the beginning of 2023:

Index at the beginning of 2023 = 97.8 * (1 + 0.315) = 97.8 * 1.315 = 128.697