The value of a condo decreases at a steady rate of 20% each year. What is the total percentage loss (to the nearest integer) in the value of the condo at the end of 2 years?
(A) 10%

(B) 24%

(C) 36%

(D) 40%

(E) 56%

The problem states that the value of a condo decreases at a rate of 20% per year. We are asked to find the total percentage loss in the condo's value after 2 years.

Let’s break it down step-by-step:

1. **Initial year decrease**: After 1 year, the condo loses 20% of its value. So, 80% of the value remains.
   - Remaining value after 1 year = $ 100\% \times 0.80 = 80\% $

2. **Second year decrease**: In the second year, the condo loses 20% of the remaining 80% value. 
   - Remaining value after 2 years = $ 80\% \times 0.80 = 64\% $

At the end of 2 years, the condo retains 64% of its original value.

3. **Total percentage loss**: 
   - Percentage loss = $ 100\% - 64\% = 36\% $

Therefore, the total percentage loss in the value of the condo at the end of 2 years is **36%**, so the correct answer is **(C) 36%**.

Would you like a detailed breakdown of why the second year reduction is applied to the reduced value, or do you have any other questions?

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**Related Questions**:
1. What if the decrease was 15% per year? How would the result change?
2. How would the percentage loss differ if we consider a 3-year period?
3. If the condo had an initial value of $500,000, what would its value be after 2 years?
4. What is the percentage loss if the rate of depreciation is 30% instead of 20%?
5. How can we calculate the total percentage loss after $ n $ years with a constant percentage decrease?

**Tip**: When dealing with percentage decreases over multiple years, always apply the percentage to the remaining value after each year, not the original value!

The value of a condo decreases at a steady rate of 20% each year. What is the total percentage loss (to the nearest integer) in the value of the condo at the end of 2 years?
(A) 10%
(B) 24%
(C) 36%
(D) 40%
(E) 56%

Find out how to calculate the total percentage loss after 2 years with a 20% annual decrease. This problem explains key mathematical concepts like percentage decrease and exponential decay, providing a detailed step-by-step solution suitable for students in Grades 8-10.

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