Math Problem Statement

Suppose your salary in 2014 is $50,000. Assuming an annual inflation rate of 3%, what salary do you need to earn in 2018 in order to have the same purchasing power? (Round your answer to two decimal places.)

Solution

To calculate the salary you would need in 2018 to have the same purchasing power as in 2014, we need to account for the effect of inflation over the 4-year period. The formula to adjust for inflation is:

Future Salary=Current Salary×(1+Inflation Rate)n\text{Future Salary} = \text{Current Salary} \times (1 + \text{Inflation Rate})^n

Where:

  • Current Salary is $50,000,
  • Inflation Rate is 3% or 0.03,
  • n is the number of years, which is 4 (from 2014 to 2018).

Now, let's calculate:

Future Salary=50,000×(1+0.03)4\text{Future Salary} = 50,000 \times (1 + 0.03)^4

Future Salary=50,000×(1.03)4\text{Future Salary} = 50,000 \times (1.03)^4

Future Salary=50,000×1.125509\text{Future Salary} = 50,000 \times 1.125509

Future Salary=56,275.45\text{Future Salary} = 56,275.45

So, to maintain the same purchasing power in 2018, you would need to earn $56,275.45.

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:

  1. How would the required salary change if the inflation rate was 4% instead of 3%?
  2. What would the salary be if the period was 5 years instead of 4 years?
  3. How would a deflation rate of 1% impact the salary calculation?
  4. What if the inflation rate varied each year? How would you calculate the necessary salary?
  5. How does inflation impact retirement savings over time?

Tip: It's always good to keep track of inflation and adjust your savings or income goals accordingly to maintain your purchasing power!

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Math Problem Analysis

Mathematical Concepts

Exponential Growth
Inflation Adjustment

Formulas

Future Salary = Current Salary × (1 + Inflation Rate)^n

Theorems

Exponential Growth Theorem

Suitable Grade Level

Grades 10-12