Let's solve both questions step by step:

Question 1: Depreciation of a computer

• Initial cost = ₹1,00,000
• Depreciation rate = 40% per year
• We need to find the cost after 2 years.

The formula for depreciation is:
$A = P(1 - r)^t$
Where:

• $A$ = Value after $t$ years
• $P$ = Initial value (₹1,00,000)
• $r$ = Depreciation rate (40% = 0.4)
• $t$ = Number of years (2 years)

Substitute the values:
$A = 1,00,000(1 - 0.4)^2$ $A = 1,00,000(0.6)^2$ $A = 1,00,000(0.36)$ $A = ₹36,000$

Answer: The cost of the computer after 2 years will be ₹36,000.

Question 2: Depreciation of a car

• Initial value = ₹75,000
• Depreciation rate = 15% per year
• We need to find the value after 3 years.

Use the same formula:
$A = P(1 - r)^t$
Where:

• $P$ = ₹75,000
• $r$ = 15% = 0.15
• $t$ = 3 years

Substitute the values:
$A = 75,000(1 - 0.15)^3$ $A = 75,000(0.85)^3$

First, calculate $0.85^3$:
$0.85^3 = 0.614125$

Now calculate $A$:
$A = 75,000 \times 0.614125$ $A ≈ ₹46,059.38$

Answer: The value of the car after 3 years will be approximately ₹46,059.38.

Summary of Answers:

1. The cost of the computer after 2 years: ₹36,000
2. The value of the car after 3 years: ₹46,059.38

Let me know if you'd like further clarifications or a detailed explanation for any step!

Related Questions:

1. How do you calculate the depreciation value for any given time period?
2. What happens if depreciation rates are compounded quarterly instead of annually?
3. How do you find the depreciation rate if the initial and final values are known?
4. How can you calculate the number of years required for a value to depreciate to half?
5. How is depreciation different for straight-line and compound methods?

Tip:

Depreciation calculations use the concept of exponential decay, so understanding the formula $A = P(1 - r)^t$ is crucial for solving similar problems.