Question

A machine costing Rd 30000 depreciation by 15% each year calculate the value of machine after five years what is the total amount of depreciation

Answer 1

Given :

Present value of the machine : 30000

Rate of depreciation : 15%

Time : 5 years

To find :

The total amount of depreciation.

Solution :

First, we should find the value of the machine after 5 years.

Value of the machine (after 5 years) :

$\sf \dashrightarrow Amount = P \bigg( 1 - \dfrac{R}{100} \bigg)^{Time}$

$\sf \dashrightarrow A = 30000 \bigg( 1 - \dfrac{15}{100} \bigg)^{5}$

$\sf \dashrightarrow A = 30000 \bigg( \dfrac{100 - 15}{100} \bigg)^{5}$

$\sf \dashrightarrow A = 30000 \bigg( \dfrac{85}{100} \bigg)^{5}$

$\sf \dashrightarrow A = 30000 \bigg( \dfrac{17}{20} \bigg)^{5}$

$\sf \dashrightarrow A = 30000 \bigg( \dfrac{17^5}{20^5} \bigg)$

$\sf \dashrightarrow A = 30000 \bigg( \dfrac{1419857}{3200000} \bigg)$

$\sf \dashrightarrow A = 3 \bigg( \dfrac{1419857}{320} \bigg)$

$\sf \dashrightarrow A = \dfrac{3 \times 1419857}{320} = \dfrac{4259571}{320}$

$\sf \dashrightarrow A = \cancel \dfrac{4259571}{320} = 13311.15$

Now, we can find the total amount of depreciation.

Total Amount of depreciation :

$\sf \dashrightarrow 30000 - 13311.15$

$\sf \dashrightarrow Ra.16688.85$

Hence, the total amount of depreciation is ₹16688.85.