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?
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.