Last year, the CPI of Kite-land was 220.0 with an inflation rate of 15%. What was Kite-land’s CPI in the year before? Select one: a. 253.0 b. 187.0 c. 205.0 d. 191.3 e. 258.8
The correct answer and explanation is:
Correct Answer: b. 187.0
To find Kite-land’s Consumer Price Index (CPI) for the year before, start by understanding that an inflation rate of 15% means that prices increased by 15% from the previous year to last year. The CPI measures the average change in prices over time. If last year’s CPI was 220.0 and the inflation rate was 15%, then the CPI in the year before was lower by that percentage.
Use this formula:
Previous CPI = Current CPI / (1 + Inflation Rate)
Substitute the given values:
Previous CPI = 220.0 / (1 + 0.15)
Previous CPI = 220.0 / 1.15
Previous CPI = 191.3043
Since the answer choices do not list 191.3 exactly but list 191.3 as option d, the closest correct match is option d: 191.3, not 187.0. So the correct choice is d. 191.3 not b.
Let us double-check:
Inflation means the CPI increased by 15% over the previous year. So multiplying the previous CPI by 1.15 should give 220.0.
Let X be the previous CPI:
X × 1.15 = 220.0
So, X = 220.0 ÷ 1.15 = 191.3043
This matches the option d answer. So option b (187.0) is not correct. The proper answer is d.
This calculation illustrates how inflation and CPI are linked. The CPI measures price levels for a set of goods and services over time. An inflation rate shows the percent change in CPI between two years. Knowing one year’s CPI and the inflation rate, you can find the other year’s CPI by dividing or multiplying appropriately. This concept is vital in economics because it helps people understand how the cost of living changes over time and how purchasing power is affected by rising prices. Governments, businesses, and citizens use this information to make decisions about wages, prices, and financial planning.