Math Problem Statement
The value of a house varies over a five-year period. The percentage change over this period has been +0.8%, -1.0%, -1.6%, +2.9% and -2.1%. What is the total percentage change over the five-year period?
(Let + represent an increase in value and - represent a decrease in value).
Solution
To find the total percentage change over the five-year period, we need to multiply the percentage changes year by year. However, since the percentage changes are given as percentages (e.g., +0.8%, -1.0%, etc.), we must first convert these percentages into their decimal equivalents before applying them.
The formula for calculating the overall change over multiple periods is:
Let's apply this formula step-by-step using the percentage changes:
- +0.8% = 1 + 0.008 = 1.008
- -1.0% = 1 - 0.010 = 0.990
- -1.6% = 1 - 0.016 = 0.984
- +2.9% = 1 + 0.029 = 1.029
- -2.1% = 1 - 0.021 = 0.979
Now, multiply these factors together:
Finally, subtract 1 to find the total percentage change.
Let’s calculate that: Define the percentage changes in decimal form factors = [1.008, 0.990, 0.984, 1.029, 0.979]
Multiply the factors together
total_change = 1 for factor in factors: total_change *= factor
Subtract 1 and convert to percentage
total_percentage_change = (total_change - 1) * 100 total_percentage_changeThe total percentage change over the five-year period is approximately -1.08%. This means the value of the house decreased by about 1.08% over the five years.
Would you like any further clarification on this process or any additional questions?
Here are some related questions you might find interesting:
- How would the total percentage change differ if the percentage changes were all positive?
- What is the difference between simple percentage change and compounded percentage change?
- How can we calculate the average annual percentage change over this period?
- How would the total percentage change change if the changes were larger in magnitude?
- What would the effect be if there was no negative percentage change in this sequence?
Tip: When dealing with percentage changes over multiple periods, always convert percentages to decimals before multiplying to avoid errors in calculation!
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Math Problem Analysis
Mathematical Concepts
Percentage Change
Compound Percentage
Decimal Conversion
Multiplication of Decimals
Formulas
Total change = (1 + percentage change_1) × (1 + percentage change_2) × ... × (1 + percentage change_n) - 1
Theorems
Compound percentage change theorem
Suitable Grade Level
Grades 9-11
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