A company purchased a processing machine for \text{₦}200,000. The value of the machine dep… — JAMB UTME

A company purchased a processing machine for $\text{₦}200,000$ . The value of the machine depreciates at a compound rate of $10\%$ per annum. At the end of $2$ years, the machine was sold at a profit of $15\%$ based on its depreciated value. What was the selling price of the machine?

A
$\text{₦}184,000$
$\text{₦}186,300$ Answer
C
$\text{₦}192,000$
D
$\text{₦}207,000$

Answer

The selling price of the machine was

\text{₦}186,300

The depreciated value after 2 years at a compound rate of

10\%

per annum is calculated as

V = 200,000 \times (0.90)^2 = \text{₦}162,000

. Selling the machine at a

15\%

profit on this depreciated value gives a selling price of

162,000 \times 1.15 = \text{₦}186,300

Step-by-Step Solution

Calculate the depreciated value of the machine after 2 years using the compound depreciation formula

V = P(1 - r)^n

V = 200,000 \times (1 - 0.10)^2 = 200,000 \times (0.90)^2 = 200,000 \times 0.81 = \text{₦}162,000

Compound depreciation reduces the asset's remaining book value by

10\%

each year.

Calculate the

15\%

profit based on the depreciated value.

\text{Profit} = 15\% \text{ of } \text{₦}162,000 = 0.15 \times 162,000 = \text{₦}24,300$.

The problem specifies that profit is made on the depreciated value.

Calculate the selling price by adding the profit to the depreciated value.

\text{Selling Price} = \text{₦}162,000 + \text{₦}24,300 = \text{₦}186,300$.

Selling price is equal to book value plus profit earned.

Key Concept

Compound Depreciation and Percentage Profit on Book Value

Estimated Time:2m 0s

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