The value of a building was Ksh.53000000 at the end of 2004 appreciated by 8% in 2005, 19% in 2006 but depreciated by 23% in 2007.
Find its value at the end of year 2005.

To find the value of the building at the end of 2005 after appreciating by 8%, we can use the following formula:

\[
\text{Value at end of 2005} = \text{Initial Value} \times (1 + \text{Percentage increase in decimal form})
\]

### Step-by-step calculation:

1. **Initial Value** at the end of 2004 = Ksh. 53,000,000
2. **Percentage appreciation** in 2005 = 8%

Convert the percentage increase into decimal form:
\[
8\% = \frac{8}{100} = 0.08
\]

Now, apply the formula:
\[
\text{Value at end of 2005} = 53,000,000 \times (1 + 0.08) = 53,000,000 \times 1.08
\]

Let’s calculate that:

\[
\text{Value at end of 2005} = 53,000,000 \times 1.08 = 57,240,000
\]

Thus, the value of the building at the end of 2005 is **Ksh. 57,240,000**.

Would you like more details or explanations on any part? Here are some related questions to consider:

1. What is the value of the building at the end of 2006 after a 19% appreciation?
2. How do you calculate depreciation for the year 2007?
3. What is the formula for compound appreciation and depreciation over multiple years?
4. How would the calculation change if the appreciation or depreciation rate were different?
5. Can the same method be applied to other assets like vehicles or equipment?

**Tip:** Always convert percentages to decimals when performing appreciation or depreciation calculations!

The value of a building was Ksh.53000000 at the end of 2004 appreciated by 8% in 2005, 19% in 2006 but depreciated by 23% in 2007. Find its value at the end of year 2005.

Discover how to calculate the value of a building that appreciated by 8% in 2005 from an initial value of Ksh. 53,000,000. This step-by-step solution explains how to perform percentage appreciation calculations, ideal for students in Grades 8-10.

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