Question

A tv was bought at rs 52,000. its value deperciated at rate of 4 % per anum.Find its value after one year​

Answer 1

QUESTION :

A TV was bought at Rs 52,000. Its value deperciated at rate of 4 % per annum. Find its value after one year.

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SOLUTION :

❖ Given :-

• Initial value of the TV at the time of purchase, V₀ = Rs. 52000

• Rate of depreciation, r = 4% p.a.

• No. of years, n = 1 year

❖ To Find :-

• Scrap value after one year, Vₙ = ?

❖ Required Formula :-

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \large{ \bold{ \: \: V_n = V_0 (1 - \frac{r}{100} ) {}^{n} \: \: }}}$

❖ Calculation :-

$\: \: \: \bigstar \: \: \: \: \sf{V_n = V_0 \: (1 - \frac{r}{100} ) {}^{n}} \: \: \: \: \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 52000 \: (1 - \frac{4}{100} ) {}^{1}} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 52000 \: (1 - \frac{4}{100} )} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 52000 \: (\frac{100 - 4}{100} )} \\ \\ \: \: \: \: \: \: \: \sf{= 52000 \times \frac{96}{100}} \\ \\ \sf{= 49920} \: \: \: \: \: \\ \\ \sf{ \therefore \: \underline{ \: V_n = Rs. \: 49920 \: }}$

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ANSWER :

The value of the TV after one year will be Rs. 49920 which was bought at Rs. 52000, depreciated at 4% per annum.

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ADDTIONAL INFORMATION :

★ Depreciation :-

Due to wear and tear, the value of certain fixed assets like car, TV, machine etc. goes on decreasing with the passage of time. The relative decrease in the value of such articles over a period of time is called the Depreciation.

• Depreciation on Rs. 100 per unit time is called the Rate of depreciation.

• Depreciated value of an article after certain year is called the Scrap value of that article.

★ Formula :-

If

• V₀ = Initial Value of the article at the time of purchase.

• Vₙ = Depreciated value after n years.

• r = Rate of depreciation.

• n = Number of years

Then,

• Vₙ = V₀ (1 - ʳ/₁₀₀) ⁿ