To determine the original value of the company's shares before the depreciation that happened over 3 years, we need to work through a step-by-step approach using the concept of compound depreciation.
### Step-by-Step Solution:
1. Understand the Depreciation Concept:
- The share price depreciated at a rate of 12% per year.
- Depreciation over multiple years compounds, meaning each year's depreciation is applied to the value after the previous year's depreciation.
2. Given Data:
- Depreciation rate per year: [tex]\(12\% = 0.12\)[/tex]
- Number of years: [tex]\(3\)[/tex]
- Present value of the shares: [tex]\( \text{Rs 8518} \)[/tex]
3. Identify the Relationship:
- The relationship between the original value [tex]\(V\)[/tex] and the present value [tex]\(P\)[/tex] after [tex]\(n\)[/tex] years with an annual depreciation rate [tex]\(d\)[/tex] is given by:
[tex]\[
P = V \times (1 - d)^n
\][/tex]
4. Rearrange to Find the Original Value:
- We need to find [tex]\(V\)[/tex]. Rearranging the formula to solve for [tex]\(V\)[/tex]:
[tex]\[
V = \frac{P}{(1 - d)^n}
\][/tex]
5. Substitute the Given Values:
- Present value ([tex]\(P\)[/tex]) = Rs 8518
- Depreciation rate ([tex]\(d\)[/tex]) = 0.12
- Number of years ([tex]\(n\)[/tex]) = 3
[tex]\[
V = \frac{8518}{(1 - 0.12)^3}
\][/tex]
6. Calculate the Compound Factor:
- Calculate [tex]\( (1 - 0.12)^3 \)[/tex]:
[tex]\[
1 - 0.12 = 0.88
\][/tex]
[tex]\[
0.88^3 = 0.681472
\][/tex]
7. Compute the Original Value:
- Finally, substitute the compound factor back into the formula to find [tex]\(V\)[/tex]:
[tex]\[
V = \frac{8518}{0.681472}
= 12499.413035311796
\][/tex]
### Conclusion:
The original value of the company's shares, before the depreciation over the 3 years, was approximately Rs 12499.41.
