Questions: Suppose your salary in 2012 is 70,000. If the annual inflation rate is 5%, what salary do you need to make in 2021 in order for it to keep up with inflation? Round your answer to the nearest cent, if necessary.

Suppose your salary in 2012 is 70,000. If the annual inflation rate is 5%, what salary do you need to make in 2021 in order for it to keep up with inflation? Round your answer to the nearest cent, if necessary.
Transcript text: Suppose your salary in 2012 is $\$ 70,000$. If the annual inflation rate is $5 \%$, what salary do you need to make in 2021 in order for it to keep up with inflation? Round your answer to the nearest cent, if necessary.
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Solution

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Solution Steps

Step 1: Convert the Annual Inflation Rate from a Percentage to a Decimal

To convert the annual inflation rate from a percentage to a decimal, we divide the given rate by 100. Thus, if the given annual inflation rate is 5%, the decimal equivalent is 5 / 100 = 0.05.

Step 2: Apply the Future Salary Formula

Using the formula \( F = S \times (1 + r)^n \), where \(S\) is the initial salary, \(r\) is the annual inflation rate in decimal form, and \(n\) is the number of years, we can calculate the future salary required to keep up with inflation. Substituting the given values: \( F = 70000 \times (1 + 0.05)^9 \).

Step 3: Round the Result

After calculating the future salary, we round the result to 2 decimal places for practical purposes. Thus, the future salary rounded is 108592.98.

Final Answer:

The future salary required to keep up with an annual inflation rate of 5% over 9 years, starting from an initial salary of 70000, is approximately 108592.98.

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