Understanding Mobile Phone Depreciation

Let's break down this problem about calculating the value of a mobile phone after it depreciates. Depreciation means that the value of an asset, like a mobile phone, decreases over time due to usage, wear and tear, or becoming outdated.

Problem Description

We are given the following information:

• Initial cost of the mobile phone: Rs. 25000
• Rate of depreciation: 5% per annum (each year)
• Time period: 2 years

We need to find the value of the mobile phone after 2 years.

How Depreciation Works Annually

When an asset depreciates at a fixed percentage each year, it's similar to compound interest, but the value decreases instead of increasing. The depreciation in the second year is calculated on the reduced value of the phone at the end of the first year, not the original cost.

Formula for Compound Depreciation

The value of an asset after 'n' years, with an initial value (Principal) 'P' and an annual depreciation rate 'r' (expressed as a decimal), is given by the formula:

\( \text{Final Value} = P \times (1 - r)^n \)

Step-by-Step Calculation of Mobile Phone Value

Let's apply the formula using the given values:

• Initial Value (P) = Rs. 25000
• Depreciation Rate (r) = 5% = \( \frac{5}{100} \) = 0.05
• Time Period (n) = 2 years

Substitute these values into the formula:

\( \text{Value after 2 years} = 25000 \times (1 - 0.05)^2 \)

\( \text{Value after 2 years} = 25000 \times (0.95)^2 \)

Now, calculate \( (0.95)^2 \):

\( (0.95)^2 = 0.95 \times 0.95 = 0.9025 \)

Finally, multiply the result by the initial value:

\( \text{Value after 2 years} = 25000 \times 0.9025 \)

\( \text{Value after 2 years} = 22562.5 \)

So, the value of the mobile phone after 2 years is Rs. 22562.50.

Comparing with Options

Let's look at the given options:

1. Rs. 22562.50
2. Rs. 23842.50
3. Rs. 24800.50
4. Rs. 21546.50

Our calculated value, Rs. 22562.50, matches the first option.

Revision Table: Key Concepts

Additional Information: Types of Depreciation

While this problem uses compound depreciation (often called reducing balance method in accounting), another common method is Straight-Line Depreciation.

• Straight-Line Depreciation: The value decreases by a fixed amount each year. The annual depreciation is calculated as \( \frac{\text{Initial Cost} - \text{Salvage Value}}{\text{Useful Life in Years}} \). Salvage value is the estimated value at the end of its useful life. This method is simpler but less often reflects the true market value decline of items like electronics.
• Reducing Balance Depreciation (Compound Depreciation): The depreciation amount decreases each year because it's a percentage of the smaller remaining value. This often reflects the market value decline of assets more accurately, especially for vehicles and electronics.

In this problem, the phrase "depreciates by 5% per annum due to its use" implies a rate applied to the current value, which is characteristic of the reducing balance method (compound depreciation).