# CLASS-9DEPRECIATION OF ARTICLE

CONCEPT OF DEPRECIATION

The value of a machine or of any other article subject to wear and tear decrease with time. Decrease in the value of an article is called it’s depreciation. Depreciation per unit of time is called the rate of depreciation.

Formulae for Depreciation

Let the present value of a machine be \$ V. let the value of this machine depreciate at R% per annum. Then –

R

a) Value of machine after n years = \$ { V X ( 1 - -------- )ⁿ}

100

V

b) Value of machine n years ago = \$ ---------------------

R

(1 - ------- )ⁿ

100

Example.1) A car was purchased two years ago. Its value depreciates at 25% per Annum. If its present value is \$ 40000, find – Its value after 3 years

Ans.) Present value of the car (V) = \$ 40000, rate of depreciation per annum (R) = 25% per annum

As per the formula -

R

Value of machine after n years = \$ { V X ( 1 - ------ )ⁿ}

100

25

=  \$ { 40000 X ( 1 - ------- )ᶟ}

100

1

=  \$ { 40000 X ( 1 - ------ )ᶟ}

4

3          3          3

=  \$ ( 40000 X ------ X ------ X ------ )

4          4          4

=  \$ 16875                 (Ans.)

Example.2) A home was purchased two years ago. Its value depreciates at 20% per Annum. If its present value is \$ 90000, find – Its value for which it was purchased 2 years ago.

V

Value of machine n years ago = \$ ------------------------

R

(1 - -------- )ⁿ

100

90000

= \$ ----------------------

20

(1 - ------- )²

100

90000

= \$ -------------------

1

(1 - ------ )²

5

90000

= \$ ---------------------

4

( ------- )²

5

5           5

=  \$  ( 90000 X ------- X ------- )

4           4

=   \$ 140625                        (Ans.)