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.

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.
Transcript text: 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. Formulas
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Solution

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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.

Step 1: Identify the Given Values

We are given:

  • Current Salary in 2015: \( \$70,000 \)
  • Annual Inflation Rate: \( 5\% \) or \( 0.05 \)
  • Number of Years: \( 2023 - 2015 = 8 \)
Step 2: Apply the Compound Interest Formula

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

Step 3: Calculate the Future Salary

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

The salary needed in 2023 to keep up with inflation is: \[ \boxed{\$103421.88} \]

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