The value of a machine depreciates at the rate of 10% per annum. It was purchased 3 years ago. If its present value is Rs. 291600, for how much was it purchased?
Let the 3 years ago machine value = P
Rate of depreciates, R = 10%
Time, n = 3 years
Now,
Value = P (1 + R/100)n [Where,
P = Present value
R = Annual interest rate
n = Time in years]
∴ Value = P (1 - 10/100)n [∵ Rate decreases]
⇒ 291600 = P (1 - 1/10)3
⇒ 291600 = P (9/10)3
⇒ 291600 = P × 729/1000
⇒ P = 291600 × 1000/729
⇒ P = 400 × 1000
⇒ P = 400000
∴ Initial value of machine is Rs.400000.