Question

the value of a machine depreciates at rate of 20% per annum. It was purchased 2 years ago. If its present value is Rs 40000 , for how much was it purchased. the answer is 62500​

Answer 1

Answer:

Step-by-step explanation:

Step 1:

Let ,

value of a machine 2 years ago, = P

Given,

Present value of machine = Rs.40000

Time, n = 2 years

Rate of depreciates, R = 20% per annum

Step 2:

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]

Step 3:

⇒ 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

Step 4:

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

Answer 2

Answer:

62500

Step-by-step explanation:

let the value of machine be x

x depricites by 20% per annum

so x*(1-20/100)²=40,000. (given)

x*(80/100)²=40,000

x=40,000*100/80=62500