if average annual tuition at public 4 - year colleges was $1,908 in 1990, when the cpi was 130.7, and $8,655…

if average annual tuition at public 4 - year colleges was $1,908 in 1990, when the cpi was 130.7, and $8,655 in 2012 when the cpi was 229.6, then the real cost of annual tuition\nrose by 158 percent during that period.\nfell by 158 percent during that period.\nrose by 354 percent during that period.\nfell by 354 percent during that period.\nrose by 75.7 percent during that period.

if average annual tuition at public 4 - year colleges was $1,908 in 1990, when the cpi was 130.7, and $8,655 in 2012 when the cpi was 229.6, then the real cost of annual tuition\nrose by 158 percent during that period.\nfell by 158 percent during that period.\nrose by 354 percent during that period.\nfell by 354 percent during that period.\nrose by 75.7 percent during that period.

Answer

Explanation:

Step1: Calculate the real cost in 1990 (using 2012 as base year)

The formula for real cost is ( \text{Real Cost}=\frac{\text{Nominal Cost}\times\text{CPI of base year}}{\text{CPI of given year}} ). For 1990, nominal cost ( C_{1990}=$1908 ), CPI of 1990 ( \text{CPI}{1990} = 130.7 ), CPI of base year (2012) ( \text{CPI}{2012}=229.6 ). ( \text{Real Cost}{1990}=\frac{1908\times229.6}{130.7}) [ \begin{align*} \text{Real Cost}{1990}&=\frac{1908\times229.6}{130.7}\ &=\frac{1908\times2296}{1307}\ &=\frac{4381728}{1307}\ &\approx$3352.51 \end{align*} ]

Step2: Calculate the percentage change

The formula for percentage change is ( \text{Percentage Change}=\frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\times 100) New value (real cost in 2012, which is nominal cost in 2012 as base year is 2012) ( C_{2012}=$8655 ), old value ( C_{1990}\approx$3352.51 ) ( \text{Percentage Change}=\frac{8655 - 3352.51}{3352.51}\times100) [ \begin{align*} \text{Percentage Change}&=\frac{5302.49}{3352.51}\times 100\ &\approx 158% \end{align*} ]

Answer:

rose by 158 percent during that period.