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Part 3: Present and Future Value (20 points)

Suppose you want to determine the value of your salary over time. Choose an annual salary amount that you would like to work with:

Part A: If the amount you chose was your salary 10 years ago, how much would it be worth today? You will need to research the CPI values needed for the calculation. (8 points)

Visit this website to find CPI values: [https://data.bls.gov/timeseries/CUUR0000SA0](https://data.bls.gov/timeseries/CUUR0000SA0)

At the top of the page next to Change Output Options, adjust the years. Annual CPI data requires all 12 months for calculation, so you must go back to the previous year. For example, if this year is 2023, use the data for 2022 as the current year, and use 2012 for 10 years ago. Check the box to "include annual averages." Click the blue "Go" button to refresh the data display and scroll down to view the table.

Using the data from the "Annual" column, record the CPI values in the spaces below.

- CPI-Current Year: ________
- CPI-10 years ago: ________

Part B: Using the current year's value from Part A, what will be the purchasing power of that amount 10 years from now, assuming inflation averages 3.10% per year? (8 points)

Part C: Using the values you calculated from Part A and Part B, which year had the better value? (4 points)

Sagot :

GinnyAnsweridn
Certainly! Let's walk through the solution step-by-step.

### Part A: Determine the Value of Your Salary Today

Given:
- Salary 10 years ago: [tex]$50,000 - CPI for the current year (2022): 292.655 - CPI for 10 years ago (2012): 229.593 To find the equivalent value of the salary today, we use the formula that adjusts the salary based on the change in the Consumer Price Index (CPI): \[ \text{Salary Today} = \text{Salary 10 Years Ago} \times \left( \frac{\text{CPI Current Year}}{\text{CPI 10 Years Ago}} \right) \] Now, plug in the values: \[ \text{Salary Today} = \$[/tex]50,000 \times \left( \frac{292.655}{229.593} \right) \]

This calculation yields:

[tex]\[ \text{Salary Today} = \$50,000 \times 1.274668652 = \$63,733.43 \][/tex]

So, the salary of [tex]$50,000 ten years ago is equivalent to $[/tex]63,733.43 today.

### Part B: Future Purchasing Power

To calculate the future value of the current salary assuming an annual inflation rate of 3.10% over 10 years, we use the formula for compound interest:

[tex]\[ \text{Future Value} = \text{Salary Today} \times \left(1 + \text{Annual Inflation Rate}\right)^{\text{Years Into Future}} \][/tex]

Given:
- Annual Inflation Rate: 3.10% or 0.031
- Years Into Future: 10
- Salary Today: [tex]$63,733.43 Plug in the values: \[ \text{Future Value} = \$[/tex]63,733.43 \times \left(1 + 0.031\right)^{10} \]

[tex]\[ \text{Future Value} = \$63,733.43 \times (1.031)^{10} \][/tex]

[tex]\[ \text{Future Value} = \$63,733.43 \times 1.358678 \][/tex]

This calculation yields:

[tex]\[ \text{Future Value} = \$63,733.43 \times 1.358678 = \$86,487.62 \][/tex]

So, in 10 years, the purchasing power of [tex]$63,733.43 today will be equivalent to $[/tex]86,487.62, assuming a 3.10% annual inflation rate.

### Part C: Comparative Value

Finally, we compare the value of the salary today and in the future:

- Salary Today: [tex]$63,733.43 - Salary 10 Years in the Future: $[/tex]86,487.62

Since [tex]$86,487.62 is greater than $[/tex]63,733.43, it indicates that the purchasing power is better 10 years in the future compared to today. Therefore, the year with the better value is 10 years in the future.

In summary:

- Current Salary Equivalent Today: [tex]$63,733.43 - Future Value in 10 Years: $[/tex]86,487.62
- Better Year for Purchasing Power: 10 Years in the Future
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