The value of a machine depreciates at the rate of 20% per annum. It wa

1.	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» 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.

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»

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.