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Due to continuous depreciation, the value of shares of a company reduces at the rate of [tex]$10\%$[/tex] per annum. In 2 years, the value of shares of a finance company becomes Rs 25,920.

a. What was the value of the shares 2 years ago?
b. How much did the value of each share of Rs 100 depreciate in 2 years?

Sagot :

GinnyAnswer
Let's tackle the problem step-by-step.

### Part (a): Finding the value of the share 2 years ago

We are given:
- The final value of the shares after 2 years, which is Rs 25920.
- The annual depreciation rate, which is 10% (0.10 in decimal form).
- The time period, which is 2 years.

The formula for depreciation is given by:
[tex]\[ \text{final\_value} = \text{initial\_value} \times (1 - \text{depreciation\_rate})^{\text{years}} \][/tex]

We need to find the initial value of the shares, denoted as [tex]\(\text{initial\_value}\)[/tex]. Rearranging the above formula to solve for [tex]\(\text{initial\_value}\)[/tex], we get:
[tex]\[ \text{initial\_value} = \frac{\text{final\_value}}{(1 - \text{depreciation\_rate})^{\text{years}}} \][/tex]

Plugging in the given values:
[tex]\[ \text{initial\_value} = \frac{25920}{(1 - 0.10)^2} \][/tex]

Calculating the expression on the denominator:
[tex]\[ (1 - 0.10)^2 = 0.90^2 = 0.81 \][/tex]

Now divide 25920 by 0.81:
[tex]\[ \text{initial\_value} = \frac{25920}{0.81} \approx 31999.999999999996 \][/tex]

So, the value of the shares 2 years ago was approximately Rs 32000.

### Part (b): Depreciation of each share of Rs 100 over 2 years

Now, we need to calculate how much a share valued at Rs 100 depreciated over 2 years at the same depreciation rate.

The formula remains the same:
[tex]\[ \text{final\_value} = \text{initial\_value} \times (1 - \text{depreciation\_rate})^{\text{years}} \][/tex]

Here, the initial value ([tex]\(\text{initial\_value}\)[/tex]) is Rs 100. The depreciation over 2 years is calculated as follows:
[tex]\[ \text{final\_value} = 100 \times (1 - 0.10)^2 \][/tex]
[tex]\[ \text{final\_value} = 100 \times 0.81 \][/tex]
[tex]\[ \text{final\_value} = 81 \][/tex]

Thus, the value of each Rs 100 share after 2 years is Rs 81. The depreciation amount is:
[tex]\[ 100 - 81 = 19 \][/tex]

So, each Rs 100 share has depreciated by Rs 19 over 2 years.

### Final Summary

(a) The value of the shares 2 years ago was approximately Rs 32000.

(b) Each Rs 100 share has depreciated by Rs 19 over 2 years.
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