Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

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.
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.