When Joe started his job at the laundromat 5 years ago, his wage was $4.50 an hour. Today his wage is $6.50 an hour. If Joe started his job in the base year, and his real wage is the same as when he started, what is the Consumer Price Index today?
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To find the Consumer Price Index (CPI) today, we need to calculate the inflation rate over the 5-year period and then adjust the current wage based on that inflation rate.
First, let's calculate the inflation rate:
Inflation rate = ((Current wage - Base wage) / Base wage) * 100
Inflation rate = (($6.50 - $4.50) / $4.50) * 100
Inflation rate = ($2.00 / $4.50) * 100
Inflation rate = 44.44%
Now, let's find the adjusted wage based on the inflation rate:
Adjusted wage = Base wage * (1 + (inflation rate / 100))
Adjusted wage = $4.50 * (1 + (44.44 / 100))
Adjusted wage = $4.50 * (1 + 0.4444)
Adjusted wage = $4.50 * 1.4444
Adjusted wage = $6.50
Since Joe's real wage today is the same as when he started, the adjusted wage is $6.50. This means that the current wage has increased by 44.44% compared to the base wage.
Now we can calculate the CPI:
CPI = (Adjusted wage / Current wage) * 100
CPI = ($6.50 / $6.50) * 100
CPI = 100
Therefore, the Consumer Price Index (CPI) today is 100.
To calculate the Consumer Price Index (CPI) and determine the answer to the question, we need to follow a few steps:
Step 1: Calculate the wage increase in terms of percentage.
The wage increase from $4.50 to $6.50 can be calculated by subtracting the old wage from the new wage and dividing by the old wage:
Wage increase = ($6.50 - $4.50) / $4.50
Step 2: Calculate the inflation rate by subtracting the wage increase from 1:
Inflation rate = 1 - Wage increase
Step 3: Calculate the CPI using the inflation rate.
The CPI can be calculated using the following formula:
CPI = 100 / (1 + inflation rate)
Now, we can calculate the answer:
Inflation rate = 1 - (($6.50 - $4.50) / $4.50)
CPI = 100 / (1 + inflation rate)
By plugging in the values:
Inflation rate = 1 - (($6.50 - $4.50) / $4.50)
= 1 - ($2.00 / $4.50)
= 1 - 0.4444444444444444
= 0.5555555555555556
CPI = 100 / (1 + 0.5555555555555556)
= 100 / 1.5555555555555556
= 64.31372549019608
Therefore, the Consumer Price Index today is approximately 64.31.