The value of a building was Ksh.40000000 at the end of 2004 appreciated by 8% in 2005, 17% in 2006 but depreciated by 25% in 2007. Find its value at the end of year 2007

To find the value of the building at the end of 2007, we will calculate the changes in value year by year, accounting for both appreciation and depreciation.

1. **Initial value at the end of 2004:**
   \[
   \text{Initial Value} = 40,000,000 \, \text{Ksh}
   \]

2. **Appreciation in 2005 by 8%:**
   \[
   \text{Value at end of 2005} = 40,000,000 \times (1 + 0.08) = 40,000,000 \times 1.08 = 43,200,000 \, \text{Ksh}
   \]

3. **Appreciation in 2006 by 17%:**
   \[
   \text{Value at end of 2006} = 43,200,000 \times (1 + 0.17) = 43,200,000 \times 1.17 = 50,544,000 \, \text{Ksh}
   \]

4. **Depreciation in 2007 by 25%:**
   \[
   \text{Value at end of 2007} = 50,544,000 \times (1 - 0.25) = 50,544,000 \times 0.75 = 37,908,000 \, \text{Ksh}
   \]

Therefore, the value of the building at the end of 2007 is **Ksh. 37,908,000**.

Would you like further explanation on any step or have any other questions?

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Here are 5 related questions to explore:

1. How would the building's value change if it depreciated by 15% instead of 25% in 2007?
2. What would the value be if there was no depreciation in 2007 but another appreciation of 10%?
3. How does a sequence of percentage increases and decreases affect an asset’s overall value?
4. If the building appreciated by 10% each year, what would be its value after three years?
5. How would compounding interest apply if the building's value was invested in a financial instrument?

**Tip:** To handle successive percentage changes, multiply the original value by the respective percentage multipliers year by year, adjusting for appreciation (greater than 1) or depreciation (less than 1).

The value of a building was Ksh. 40,000,000 at the end of 2004 appreciated by 8% in 2005, 17% in 2006 but depreciated by 25% in 2007. Find its value at the end of year 2007.

Find out how the value of a building changes over time through appreciation and depreciation. This problem details the step-by-step process of calculating successive percentage changes for a building initially valued at Ksh. 40,000,000 at the end of 2004, with 8% appreciation in 2005, 17% in 2006, and a 25% depreciation in 2007, resulting in a final value of Ksh. 37,908,000 by the end of 2007.

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