Question

The value of a machine depreciates at the rate of 20% per annum. It was purchased 2 years ago. If its present value is Rs. 40000 for how much was it purchased? 

A. Rs. 56000 

B. Rs. 62500 

C. Rs. 65200 

D. Rs. 56500

Answer 1

Let value of a machine 2 years ago, = P

Present value of machine = Rs.40000

Time, n = 2 years 

Rate of depreciates, R = 20% per annum 

Now, 

Amount (A) = P (1 + R/100)ⁿ [Where, A = Amount with compound interest 

P = Present value 

R = Annual interest rate 

n = Time in years] 

∴ Value = P (1 - R/100)ⁿ [∵ Rate decreases] 

⇒ 40000 = P (1 - 20/100)² 

⇒ 40000 = P (1 - 1/5)² 

⇒ 40000 = P (4/5)² 

⇒ 40000 = P × 16/25 

⇒ P = 40000 × 25/16 

⇒ P = 2500 × 25 

⇒ P = 62500 

∴ Value of a machine 2 years ago is Rs.62500.