To determine the salary needed in 2016 to maintain the same purchasing power as [tex]$40,000 in 2014, given an annual inflation rate of 9%, we need to follow these steps:
1. Identify the initial salary:
The salary in 2014 is $[/tex]40,000.
2. Identify the inflation rate:
The annual inflation rate is 9%.
3. Determine the number of years:
We need to calculate the salary for 2016, which is 2 years away from 2014.
4. Account for inflation over the years:
The formula to adjust the salary for inflation is:
[tex]\[
\text{Future Salary} = \text{Initial Salary} \times (1 + \text{Inflation Rate})^{\text{Number of Years}}
\][/tex]
5. Plug in the values:
[tex]\[
\text{Future Salary} = 40000 \times (1 + 0.09)^2
\][/tex]
6. Calculate the future salary:
[tex]\[
\text{Future Salary} = 40000 \times (1.09)^2
\][/tex]
[tex]\[
\text{Future Salary} = 40000 \times 1.1881
\][/tex]
[tex]\[
\text{Future Salary} \approx 47524.0
\][/tex]
Therefore, to have the same purchasing power in 2016 as you had with [tex]$40,000 in 2014, you would need to earn approximately $[/tex]47,524.00.
