Questions: You wish to retire in forty years. Currently, your annual living expenses are 40,000 per year. (Round your answer to the nearest cent. Refer to Chapter 11, Section 2) Assuming an annual inflation rate of 3.5%, how much will your annual living expenses be in 40 years?

Solution Steps

To determine the future value of your annual living expenses given an annual inflation rate, we can use the formula for compound interest. The formula is:

\[ FV = PV \times (1 + r)^n \]

where:

• \( FV \) is the future value of the annual living expenses.
• \( PV \) is the present value of the annual living expenses (\$40,000).
• \( r \) is the annual inflation rate (3.5% or 0.035).
• \( n \) is the number of years (40).

We are given the following values:

• Present value of annual living expenses (\( PV \)): \$40,000
• Annual inflation rate (\( r \)): 3.5% or 0.035
• Number of years (\( n \)): 40

To find the future value (\( FV \)) of the annual living expenses, we use the compound interest formula: \[ FV = PV \times (1 + r)^n \]

Substitute the given values into the formula: \[ FV = 40000 \times (1 + 0.035)^{40} \]

Perform the calculation: \[ FV = 40000 \times (1.035)^{40} \] \[ FV \approx 40000 \times 3.9593 \] \[ FV \approx 158370.3888 \]

Final Answer