Question

(c) If an automobiles depreciates in balues 5% every year, at the end of 4 years what is the value of the automobile purchased for Rs.12,000/-? (
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Answer 1

Given:

An automobile depreciates in values 5% every year, at the end of 4 years

To find:

What is the value of the automobile purchased for Rs.12,000/- at the end of 4 years?

Solution:

To solve the above-given problem we will use the following formula of depreciation:

$\boxed{\boxed{\bold{D = P[1 - \frac{R}{100} ]^n}}}$

where

"D" → the depreciated value

"P" → the present value

"R" → the rate of depreciation

"n" → no. of years

The cost of the automobile = Rs. 12000

The rate of depreciation = 5% every year

Time = 4 years

Now, by substituting the given values in the formula of the depreciation is,

$D = 12000 [1 - \frac{5}{100} ]^4$

$\implies D = 12000\times [\frac{100 - 5}{100} ]^4$

$\implies D = 12000\times [\frac{95}{100} ]^4$

$\implies D = 12000\times \frac{95}{100} \times \frac{95}{100} \times \frac{95}{100} \times \frac{95}{100}$

$\implies D = 12\times 95 \times \frac{95}{10} \times \frac{95}{100} \times \frac{95}{100}$

$\implies D = 12\times 95 \times 9.5 \times 0.95\times 0.95$

$\implies \bold{D = 9774.07}$

Thus, at the end of 4 years, the value of the automobile will be →

Rs. 9774.07.

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