Question

A piece of machinery depreciated depriciates 6000 the first year, 5700 the second year and 5400 the third year. If the rate of depreciation is constant, what is the amount of depreciation of the piece of machinery in the sixth year?

Answer 1

Answer:

The amount of depreciation of piece of machine after 6 years is 4,410 unit  .

Step-by-step explanation:

Given as :

The first year depreciation amount = 6000

The second year depreciation amount = 5700

The third year depreciation amount = 5400

let the rate of depreciation = R

I.e R = $\dfrac{\textrm initial value - \textrm afinal value}{\textrm initial value}$ × 100

or, R = $\frac{6000-5700}{5000}$  × 100

Or R = $\frac{300}{5000}$  × 100

So , R = 5 %

This rate of depreciation is constant

Time period = 6 years

Now,

Value of machine after n years = initial value × $(1-\dfrac{\textrm rate}{100})^{n}$

or, Value of machine after 6 years = 6000 × $(1-\dfrac{\textrm 5}{100})^{6}$

Or, Value of machine after 6 years = 6000 × $(0.95)^{6}$

∴ Value of machine after 6 years = 6000 × 0.7350

I.e Value of machine after 6 years = 4,410

Hence The amount of depreciation of piece of machine after 6 years is 4,410 unit  . Answer