Annual CPI values
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
184.00
188.9
195.3
201.6
207.342
215.303
214.537
218.056
224.939
229.594
232.957
Ivy Tech Tuition was $87.66 per credit hour in 2006. Use the CPI values to determine what the school would be charging in 2013 if they only increased tuition based on inflation. (round to the nearest cent)
To determine what Ivy Tech would be charging in 2013 if they only increased tuition based on inflation, we need to calculate the inflation rate between 2006 and 2013 using the Consumer Price Index (CPI) values given.
The formula to calculate the inflation rate is:
Inflation Rate = (CPI in the year you want to know the value / CPI in the base year) * 100
Using this formula, we can calculate the inflation rate from 2006 to 2013:
Inflation Rate = (CPI in 2013 / CPI in 2006) * 100
= (232.957 / 207.342) * 100
= 112.41
This means that there was a 112.41% increase in prices from 2006 to 2013.
Now, let's calculate what Ivy Tech would be charging in 2013 if they increased tuition based on this inflation rate:
New Tuition = Old Tuition + (Old Tuition * Inflation Rate / 100)
Old Tuition = $87.66 (per credit hour in 2006)
Inflation Rate = 112.41%
New Tuition = $87.66 + ($87.66 * 112.41 / 100)
= $87.66 + ($98.60)
= $186.26
Therefore, if Ivy Tech only increased tuition based on inflation, they would be charging $186.26 per credit hour in 2013.
To determine what Ivy Tech tuition would be in 2013 based on inflation, we first need to calculate the inflation rate for each year from 2006 to 2013. The formula to calculate the inflation rate is:
Inflation rate = (CPI in year 2 - CPI in year 1) / CPI in year 1
Using the CPI values given, we can calculate the inflation rate for each year:
Inflation rate for 2007 = (207.342 - 201.6) / 201.6 = 0.0285
Inflation rate for 2008 = (215.303 - 207.342) / 207.342 = 0.0384
Inflation rate for 2009 = (214.537 - 215.303) / 215.303 = -0.0036
Inflation rate for 2010 = (218.056 - 214.537) / 214.537 = 0.0164
Inflation rate for 2011 = (224.939 - 218.056) / 218.056 = 0.0316
Inflation rate for 2012 = (229.594 - 224.939) / 224.939 = 0.0207
Next, we need to calculate the cumulative inflation rate from 2006 to 2013:
Cumulative inflation rate = (1 + inflation rate for each year) * (1 + inflation rate for each year) * ... * (1 + inflation rate for each year)
Cumulative inflation rate = (1 + 0.0285) * (1 + 0.0384) * (1 - 0.0036) * (1 + 0.0164) * (1 + 0.0316) * (1 + 0.0207)
Cumulative inflation rate = 1.1945
Now, we can calculate the Ivy Tech tuition in 2013 using the formula:
Tuition in 2013 = Tuition in 2006 * Cumulative inflation rate
Tuition in 2013 = $87.66 * 1.1945
Tuition in 2013 = $104.75 (rounded to the nearest cent)
Therefore, if Ivy Tech only increased tuition based on inflation, they would be charging approximately $104.75 per credit hour in 2013.