High School

A machine depreciates by 20% each year. If the initial value is Rs. 15625, what is the estimated value at the end of 5 years?

a. Rs. 3125
b. Rs. 5000
c. Rs. 4000
d. Rs. 8000

Answer :

Final answer:

The estimated value of a machine with an initial value of Rs. 15625 after 5 years of depreciating at 20% annually is approximately Rs. 5000.

Explanation:

The question involves calculating the depreciation of a machine over 5 years with an annual depreciation rate of 20%. To estimate the value of the machine after 5 years, we apply the depreciation formula:

Value after n years = Initial value × (1 - depreciation rate)^n

Given the initial value of Rs. 15625 and a depreciation rate of 0.2 (20%), we get:

Value after 5 years = 15625 × (1 - 0.2)^5

Value after 5 years = 15625 × (0.8)^5

Value after 5 years = 15625 × (0.32768)

Value after 5 years = Rs. 5120 (approx)

The closest answer to this calculated value is option c, Rs. 5000. Therefore, the estimated value of the machine at the end of 5 years is Rs. 5000.