Questions: Suppose your salary in 2015 is 70,000. If the annual inflation rate is 5%, what salary do you need to make in 2023 in order for it to keep up with inflation? Round your answer to the nearest cent, if necessary.

Solution Steps

To determine the salary needed in 2023 to keep up with inflation, we can use the formula for compound interest, which is also applicable to inflation adjustments. The formula is:

\[ \text{Future Salary} = \text{Current Salary} \times (1 + \text{Inflation Rate})^{\text{Number of Years}} \]

Given:

• Current Salary in 2015 = \$70,000
• Annual Inflation Rate = 5% (or 0.05)
• Number of Years = 2023 - 2015 = 8

We will plug these values into the formula to calculate the future salary.

We are given:

• Current Salary in 2015: \( \$70,000 \)
• Annual Inflation Rate: \( 5\% \) or \( 0.05 \)
• Number of Years: \( 2023 - 2015 = 8 \)

To find the future salary that keeps up with inflation, we use the compound interest formula: \[ \text{Future Salary} = \text{Current Salary} \times (1 + \text{Inflation Rate})^{\text{Number of Years}} \]

Substituting the given values: \[ \text{Future Salary} = 70000 \times (1 + 0.05)^8 \]

First, calculate the growth factor: \[ (1 + 0.05)^8 = 1.477455 \]

Then, multiply by the current salary: \[ \text{Future Salary} = 70000 \times 1.477455 = 103421.8811 \]

Final Answer