The Consumer Price Index (CPI) is a measure of the average change in price over time from a designated reference period, at which it equals 100. The index is based on prices of basic consumer goods and services. The table provided lists the CPI for several years from 1960 to 2021.
If the price change in cars parallels the change in the CPI, what would a car sell for in 2021 if a comparable model sold for $15,500 in 1999?
| Year | CPI |
|---|---|
| 1960 | 29.6 |
| 1973 | 44.4 |
| 1986 | 109.6 |
| 1999 | 156.9 |
| 2012 | 229.6 |
| 2021 | 271.0 |
In 2021, a comparable car would sell for approximately $____ (Round to the nearest dollar as needed).
Answer (2)
To calculate the approximate selling price of a car in 2021, given that it sold for $15,500 in 1999 and the price change parallels the change in the Consumer Price Index (CPI), follow these steps:
Identify the CPI values for the relevant years:
CPI in 1999 = 156.9
CPI in 2021 = 271.0
Calculate the rate of change in the CPI from 1999 to 2021:
Rate of Change = CPI in 1999 CPI in 2021 = 156.9 271.0
Compute the rate of change:
Rate of Change ≈ 1.729
Estimate the price of the car in 2021 based on the rate of change:
Price in 2021 = Price in 1999 × Rate of Change = 15 , 500 × 1.729
Calculate the estimated price:
Price in 2021 ≈ 26 , 819.5
Round to the nearest dollar:
The car would sell for approximately $26,820 in 2021.
By following these steps, you can see that the calculations allow us to adjust the original 1999 price based on the change in the CPI to estimate a comparable price in 2021.
The estimated selling price of a car in 2021, based on a comparable model selling for $15,500 in 1999, is approximately $26,820. This estimate uses the proportions of the Consumer Price Index (CPI) changes over that time. The calculation involves determining the rate of change in CPI and applying it to the original price.
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