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Sajan bought a laptop for Rs 75,000. The price of the laptop depreciates at the rate of [tex]$10\%$[/tex] p.a.

(i) What does [tex]$R$[/tex] represent in the formula for the price after [tex]$T$[/tex] years, [tex]$V_{T} = V \left(1-\frac{R}{100}\right)^{T}$[/tex]?

(ii) What will be the price of the laptop after 2 years?

(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?

Sagot :

GinnyAnswer
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.
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