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Difficulty: MediumFinancial Mathematics (Interest, Profit, Loss, and Depreciation)

An entrepreneur bought a commercial printing machine for ₦300,000\text{₦}300,000. If the machine depreciates in value at a compound rate of 15%15\% per annum, what is its value in Naira (₦\text{₦}) at the end of 22 years?

Answer: 216750 ₦

Answer

The value of the machine at the end of 2 years is ₦216,750.
The value of the asset after 2 years is calculated using the reducing balance formula: V2=V0(1−r)2=300,000(0.85)2=₦216,750V_2 = V_0(1 - r)^2 = 300,000(0.85)^2 = \text{₦}216,750.

Step-by-Step Solution

1
Identify given parameters
Initial principal value V0=300,000V_0 = 300,000, annual depreciation rate r=0.15r = 0.15, duration n=2n = 2 years.
Establishing known variables simplifies formula substitution.
2
Apply compound depreciation formula
V2=V0(1−r)2=300,000(1−0.15)2V_2 = V_0(1 - r)^2 = 300,000(1 - 0.15)^2
Asset values decrease multiplicatively per period under compound depreciation.
3
Compute the final depreciated value
V2=300,000×(0.85)2=300,000×0.7225=216,750V_2 = 300,000 \times (0.85)^2 = 300,000 \times 0.7225 = 216,750
Multiplying the initial amount by the combined depreciation factor yields the residual asset value.

Key Concept

Compound Depreciation
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Topics

Financial Mathematics (Interest, Profit, Loss, and Depreciation)

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