Question

the value of machine depreciates at rate of 5% per annum. it was purchased 3 years ago. if it's present value is 965300. for how much was it purchased​

Answer 1

Given:

The value of the machine depreciates at a rate of 5% per annum.

It was purchased 3 years ago. if it's present value is 965300.

To find:

For how much was it purchased​?

Solution:

We know the formula of depreciation in the price of an article is:

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

where A = present value, P = value before n years, R = rate of depreciation and n = no. of years.

The present value of the machine, A = Rs. 965300

The rate of depreciation, R = 5%

The no. of years, n = 3 years

The value of the machine at the time of purchase be "P".

Now, on substituting the given value in the formula above, we get

$965300 = P [1 - \frac{5}{100} ]^3$

$\implies 965300 = P [\frac{95}{100} ]^3$

$\implies P = 965300 \times \frac{100^3}{95^3}$

$\implies \bold{P = 1125878.40}$

Thus, the machine was purchased for Rs. 1125878.40.

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