Question

in 1983, a winter hat cost $12.95. today, a winter hat costs $24.50. if the cpi is 219, what is the percent relation of the actual price of a winter hat to the expected price?
a. the actual price is 39.3% higher than the expected price.
b. the actual price is 15.8% higher than the expected price.
c. the actual price is 13.6% lower than the expected price.
d. the actual price is 29.8% lower than the expected price.

Explanation:

Calculate the expected price of the hat today

Using the Consumer Price Index and Inflation Adjustment knowledge points

$$ \text{Expected Price} = \text{Price in 1983} \times \frac{\text{CPI Today}}{100} = 12.95 \times \frac{219}{100} = 28.3605 \approx \$28.36 $$

Calculate the percent relation of actual to expected price

Using the Inflation Adjustment knowledge point

$$ \text{Percent Difference} = \frac{\text{Actual Price} - \text{Expected Price}}{\text{Expected Price}} \times 100 = \frac{24.50 - 28.3605}{28.3605} \times 100 \approx -13.61\% $$

This means the actual price is approximately \(13.6\%\) lower than the expected price.

Answer:

• a. The actual price is 39.3% higher than the expected price.
• b. The actual price is 15.8% higher than the expected price.
• c. The actual price is 13.6% lower than the expected price. (Correct answer)
• d. The actual price is 29.8% lower than the expected price.