Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.
Sagot :
Sure, let's go through each part of the question step by step.
### Given:
- Initial cost of the laptop: [tex]\( Rs \, 75,000 \)[/tex]
- Depreciation rate per annum: [tex]\( 10\% \)[/tex]
### (i) What does [tex]\( R \)[/tex] represent in the price after [tex]\( T \)[/tex] years [tex]\( V_T = V \left( 1 - \frac{R}{100} \right)^T \)[/tex]?
In the formula [tex]\( V_T = V \left( 1 - \frac{R}{100} \right)^T \)[/tex]:
- [tex]\( V \)[/tex] is the initial cost of the laptop, which is [tex]\( Rs \, 75,000 \)[/tex].
- [tex]\( R \)[/tex] is the annual depreciation rate in percentage. In this case, [tex]\( R = 10 \% \)[/tex].
- [tex]\( T \)[/tex] is the number of years after which we want to find the depreciated value.
Therefore, [tex]\( R \)[/tex] represents the annual depreciation rate in percentage.
### (ii) What will be the price of the laptop after 2 years?
Using the formula:
[tex]\[ V_T = V \left( 1 - \frac{R}{100} \right)^T \][/tex]
For [tex]\( T = 2 \)[/tex] years:
- [tex]\( V = 75000 \)[/tex]
- [tex]\( R = 10 \)[/tex]
- [tex]\( T = 2 \)[/tex]
Substituting the values:
[tex]\[ V_2 = 75000 \left( 1 - \frac{10}{100} \right)^2 \][/tex]
[tex]\[ V_2 = 75000 \left( 0.90 \right)^2 \][/tex]
[tex]\[ V_2 = 75000 \times 0.81 \][/tex]
[tex]\[ V_2 = 60750.00000000001 \][/tex]
So, the price of the laptop after 2 years will be [tex]\( Rs \, 60750.00 \)[/tex].
### (iii) If he sold the laptop after 3 years at the same rate of compound depreciation, how much less amount would he get than if it was sold after 2 years?
First, we need to calculate the price of the laptop after 3 years:
For [tex]\( T = 3 \)[/tex] years:
- [tex]\( V = 75000 \)[/tex]
- [tex]\( R = 10 \)[/tex]
- [tex]\( T = 3 \)[/tex]
Substituting the values:
[tex]\[ V_3 = 75000 \left( 1 - \frac{10}{100} \right)^3 \][/tex]
[tex]\[ V_3 = 75000 \left( 0.90 \right)^3 \][/tex]
[tex]\[ V_3 = 75000 \times 0.729 \][/tex]
[tex]\[ V_3 = 54675.00000000001 \][/tex]
So the price of the laptop after 3 years will be [tex]\( Rs \, 54675.00 \)[/tex].
Now, let's find the difference between the price after 2 years and the price after 3 years:
[tex]\[ \text{Difference} = 60750.00000000001 - 54675.00000000001 \][/tex]
[tex]\[ \text{Difference} = 6075.00 \][/tex]
So, if he sells the laptop after 3 years, he would get [tex]\( Rs \, 6075.00 \)[/tex] less than if it was sold after 2 years.
### Given:
- Initial cost of the laptop: [tex]\( Rs \, 75,000 \)[/tex]
- Depreciation rate per annum: [tex]\( 10\% \)[/tex]
### (i) What does [tex]\( R \)[/tex] represent in the price after [tex]\( T \)[/tex] years [tex]\( V_T = V \left( 1 - \frac{R}{100} \right)^T \)[/tex]?
In the formula [tex]\( V_T = V \left( 1 - \frac{R}{100} \right)^T \)[/tex]:
- [tex]\( V \)[/tex] is the initial cost of the laptop, which is [tex]\( Rs \, 75,000 \)[/tex].
- [tex]\( R \)[/tex] is the annual depreciation rate in percentage. In this case, [tex]\( R = 10 \% \)[/tex].
- [tex]\( T \)[/tex] is the number of years after which we want to find the depreciated value.
Therefore, [tex]\( R \)[/tex] represents the annual depreciation rate in percentage.
### (ii) What will be the price of the laptop after 2 years?
Using the formula:
[tex]\[ V_T = V \left( 1 - \frac{R}{100} \right)^T \][/tex]
For [tex]\( T = 2 \)[/tex] years:
- [tex]\( V = 75000 \)[/tex]
- [tex]\( R = 10 \)[/tex]
- [tex]\( T = 2 \)[/tex]
Substituting the values:
[tex]\[ V_2 = 75000 \left( 1 - \frac{10}{100} \right)^2 \][/tex]
[tex]\[ V_2 = 75000 \left( 0.90 \right)^2 \][/tex]
[tex]\[ V_2 = 75000 \times 0.81 \][/tex]
[tex]\[ V_2 = 60750.00000000001 \][/tex]
So, the price of the laptop after 2 years will be [tex]\( Rs \, 60750.00 \)[/tex].
### (iii) If he sold the laptop after 3 years at the same rate of compound depreciation, how much less amount would he get than if it was sold after 2 years?
First, we need to calculate the price of the laptop after 3 years:
For [tex]\( T = 3 \)[/tex] years:
- [tex]\( V = 75000 \)[/tex]
- [tex]\( R = 10 \)[/tex]
- [tex]\( T = 3 \)[/tex]
Substituting the values:
[tex]\[ V_3 = 75000 \left( 1 - \frac{10}{100} \right)^3 \][/tex]
[tex]\[ V_3 = 75000 \left( 0.90 \right)^3 \][/tex]
[tex]\[ V_3 = 75000 \times 0.729 \][/tex]
[tex]\[ V_3 = 54675.00000000001 \][/tex]
So the price of the laptop after 3 years will be [tex]\( Rs \, 54675.00 \)[/tex].
Now, let's find the difference between the price after 2 years and the price after 3 years:
[tex]\[ \text{Difference} = 60750.00000000001 - 54675.00000000001 \][/tex]
[tex]\[ \text{Difference} = 6075.00 \][/tex]
So, if he sells the laptop after 3 years, he would get [tex]\( Rs \, 6075.00 \)[/tex] less than if it was sold after 2 years.
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.
