A retired couple has a fixed income of $3,100 per month. Assuming an annual inflation rate of 9% (compounded annually), what is the purchasing power (in dollars) of their monthly income in 5 years? (Round your answer to the nearest cent.)

To find the purchasing power of the couple's monthly income in 5 years, we need to account for the effect of inflation on their fixed income. Inflation reduces the purchasing power of money over time, and this reduction can be calculated using the formula for the future value of money with inflation:

\[
\text{Purchasing Power} = \frac{\text{Current Income}}{(1 + \text{Inflation Rate})^n}
\]

Where:
- Current Income = \$3,100 per month
- Inflation Rate = 9% (or 0.09 as a decimal)
- $n$ = 5 years

Plugging in the values:

\[
\text{Purchasing Power} = \frac{3100}{(1 + 0.09)^5}
\]

Now, let's calculate this value:

\[
\text{Purchasing Power} = \frac{3100}{(1.09)^5}
\]

Calculating the value of $ (1.09)^5 $:

\[
(1.09)^5 \approx 1.53862
\]

So, the purchasing power is:

\[
\text{Purchasing Power} = \frac{3100}{1.53862} \approx 2015.20
\]

Therefore, the purchasing power of their monthly income in 5 years, rounded to the nearest cent, is approximately **$2,015.20**.

Would you like further details or have any questions?

Here are some related questions that expand on this topic:

1. How does changing the inflation rate affect the purchasing power in 5 years?
2. What would the purchasing power be in 10 years with the same inflation rate?
3. How would different compounding intervals (e.g., monthly instead of annually) affect the calculation?
4. How much should their monthly income increase each year to maintain the same purchasing power?
5. What if the couple's income increased by a fixed percentage each year? How would that affect their purchasing power?

**Tip:** Inflation is compounded, so even small increases in the inflation rate can significantly affect long-term purchasing power.

Learn how to calculate the purchasing power of a retired couple's $3,100 monthly income over 5 years, accounting for a 9% annual inflation rate. This problem involves inflation adjustments and exponential decay, using the formula for compounding. Suitable for high school students (Grades 10-12).

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