The value of a machine depreciates at the rate of 10% per annum. It was purchased 3 years ago for Rs. 60000. What is the present value of the machine?
Value of a machine 3 years ago, P = Rs.60000
Time, n = 3 years
Rate of depreciates, R = 10% 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]
= 60000 (1 - 10/100)3
= 60000 (1 - 1/10)3
= 60000 (9/10)3
= 60000 × 9/10 × 9/10 × 9/10
= 60 × 9 × 9 × 9
= 43740
∴ Present value of the machine is Rs.43740.