Lesson 54: Compound Percent & Successive Change

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

This lesson focuses on calculating compound percent changes and understanding successive increases or decreases applied to quantities over multiple steps. Real-world applications include finance, discounts, and population growth.

Learning Objectives

• Calculate successive percent increases and decreases.
• Understand compound percent change formulas.
• Apply these methods to practical real-world scenarios.

Topics Covered

• Successive percent increase and decrease
• Compound percent change formula: Final = Original × (1 ± p1) × (1 ± p2) ...
• Applications in price changes, discounts, and interest

Key Terms

• Compound Percent Change: The overall change after applying multiple successive percent changes.
• Successive Increase: Increasing a value multiple times in sequence, each on the previous result.
• Successive Decrease: Decreasing a value multiple times in sequence, each on the previous result.

Lesson Examples

Example 1: Successive Increase

1. An item costs $100. It increases by 10% in year 1 and 5% in year 2. Find the final price.
2. Year 1: 100 × 1.10 = 110
3. Year 2: 110 × 1.05 = 115.50
4. Final Price: $115.50

Example 2: Successive Decrease

1. A population of 2000 decreases by 5% in year 1 and 10% in year 2. Find the final population.
2. Year 1: 2000 × 0.95 = 1900
3. Year 2: 1900 × 0.90 = 1710
4. Final Population: 1710

Practice Problems

1. An item's price is $150. It is increased by 8% and then decreased by 5%. Find the final price.
2. A salary of $3000 is increased by 5% and then increased by 3%. Calculate the new salary.
3. A population of 5000 decreases by 4% each year for two consecutive years. Find the final population.
4. An investment of $1000 grows by 6% in the first year and 4% in the second year. Calculate the final value.

Tips & Common Mistakes

• Always apply each percent change to the most recent value, not the original.
• Convert percentages to decimals before multiplying.
• Do not simply add or subtract the percentages; compound change multiplies them.

Summary

Compound percent change allows you to calculate the effect of multiple successive increases or decreases on a quantity. It is used in finance, population studies, and pricing calculations.

Challenge Problems

1. A product price is increased by 12% and then 15%. Calculate the final price if the original price was $250.
2. A population decreases by 7% one year and increases by 5% the next. If the initial population is 10,000, find the final population.
3. An investment grows by 10% per year for 3 consecutive years. What is the total percent increase?