**Annual Inflation Rate**

Year2 Percent4 Percent6 Percent8 Percent10 Percent2022

$ 1,000

$ 1,000

$ 1,000

$ 1,000

$ 1,000

2023

980

962

943

926

909

2024

961

925

890

857

826

2025

942

889

840

794

751

2026

924

855

792

735

683

2027

906

822

747

681

621

2028

888

790

705

630

564

2029

871

760

665

584

513

2030

853

731

627

540

467

2031

837

703

592

500

424

2032

820

676

558

463

386

Using the table, what will the *real* value of $100 be in 7 years if you hide the money under your mattress and the inflation rate is

**Instructions:** Round your responses to two decimal places. Assume you hid the money under your mattress in 2022.

2%.

$ 

6%.

$ 

10%.

$ 

To find the real value of $100 after 7 years under different inflation rates, we need to follow this approach:

1. The real value of money decreases due to inflation. The formula to calculate the real value $ V $ of money after a certain number of years given the inflation rate is:

\[
V = \frac{100}{\text{{Value in year 7 as a fraction of initial value}}}
\]

Looking at the table provided, we observe how $1000 depreciates over 7 years for different inflation rates.

### 1. **For 2% inflation**:
- In 2029 (7 years later), the value of $1000 is \$871.
- Thus, the real value of $100 in 7 years is calculated by the ratio:

\[
V = 100 \times \frac{871}{1000} = 87.10
\]

### 2. **For 6% inflation**:
- In 2029, the value of $1000 is \$665.
- Thus, the real value of $100 in 7 years is:

\[
V = 100 \times \frac{665}{1000} = 66.50
\]

### 3. **For 10% inflation**:
- In 2029, the value of $1000 is \$513.
- Thus, the real value of $100 in 7 years is:

\[
V = 100 \times \frac{513}{1000} = 51.30
\]

### Final Answers:
1. **For 2% inflation:** $87.10
2. **For 6% inflation:** $66.50
3. **For 10% inflation:** $51.30

Would you like more details or clarifications on any part? 

Here are 5 related questions:
1. How does inflation affect purchasing power over time?
2. What happens if inflation is higher than the rate of return on savings?
3. How do governments control inflation?
4. What is the difference between nominal and real interest rates?
5. How do compound interest and inflation interact over long periods?

**Tip:** To preserve the value of money over time, consider investing in inflation-protected securities or assets that typically outpace inflation.

Using the table, what will the real value of $100 be in 7 years if you hide the money under your mattress and the inflation rate is: 2%, 6%, and 10%?

Discover how to calculate the real value of $100 over 7 years when exposed to inflation rates of 2%, 6%, and 10%. Follow step-by-step solutions using real value formulas and percentage depreciation from the given data. This problem is suitable for high school students in Grades 9-12.

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