An amount of money loses value due to inflation. $100 is only worth $90 after 2 years and $87 after 3 years. Find the inflation rate for the 3rd year.

To find the inflation rate for the 3rd year, we'll follow these steps:

1. **Determine the value of the money at the end of the 2nd year**:  
   The value after 2 years is given as $90.

2. **Determine the value of the money at the end of the 3rd year**:  
   The value after 3 years is given as $87.

3. **Calculate the inflation rate for the 3rd year**:  
   The inflation rate can be found by comparing the decrease in value from the 2nd year to the 3rd year.

   \[
   \text{Inflation Rate (3rd year)} = \frac{\text{Value at end of 2nd year} - \text{Value at end of 3rd year}}{\text{Value at end of 2nd year}} \times 100
   \]

   Substituting the values:

   \[
   \text{Inflation Rate (3rd year)} = \frac{90 - 87}{90} \times 100 = \frac{3}{90} \times 100 \approx 3.33\%
   \]

The inflation rate for the 3rd year is approximately **3.33%**.

Would you like further details on this calculation or have any questions? Here are some related questions to consider:

1. How does compounding inflation affect the value of money over multiple years?
2. What would be the inflation rate if the value after 4 years was $85?
3. How do different methods of calculating inflation (e.g., CPI) compare to this basic approach?
4. Can inflation rates be negative? If so, what does that indicate?
5. How does the real interest rate relate to the inflation rate?

**Tip:** Understanding the concept of inflation helps in financial planning, as it impacts the real value of savings and investments over time.

Learn how to calculate the inflation rate when $100 loses value to $87 over 3 years. Understand the percentage change formula applied to finance scenarios. Suitable for high school students and anyone interested in financial calculations.

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