Suppose your grandfather earned a salary of $12,000 in 1964. If the CPI is 31 in 1964 and 219 in 2016, then the value of your grandfather's salary in 2016 dollars is approximately

Accepted Solution

Answer:$ 8477.42 ( approx )Step-by-step explanation:Since, the CPI formula is,[tex]\text{CPI}=\frac{\text{Cost in current year}}{\text{Cost in base year}}\times 100[/tex]Given,In 1964, CPI is 31 and cost is $12,000,By substituting values,[tex]31=\frac{12000}{\text{Cost in base year}}\times 100[/tex][tex]\implies \text{Cost in base year}=\frac{1200000}{31}[/tex]In 2016, CPI is 219, Since, the cost in base year is constant,[tex]\implies 219=\frac{\text{Cost in current year}}{\frac{1200000}{31}}[/tex][tex]\implies \text{Cost in current year}=219\times \frac{1200000}{31}=8477.41935484\approx 8477.42[/tex]Hence, the salary in 2016 would be $ 8,477.42. ( approx )