Mathematics 2018 JAMB Past Questions - Question 25: A machine valued at #20,000 depreciates by 10% every year. what will be the value of the machine at the end of two years?

Correct Answer

A

Explanation

Year 1 depreiation 20,000 x 10/100 = 2,000Value at the end of year 1 = 20000 - 2000 = 18,00Depreciation in year 2 = 18,000 x 10/100 = 1,800Value at the end of two years= 20,000 - (2000+1800)= 20,000 - 3800 = # 16200To find the value of the machine at the end of two years, we can use the formula for depreciation:\[ \text{Value after depreciation} = \text{Initial value} \times (1 - \text{Depreciation rate})^{\text{Number of years}} \]In this case, the initial value of the machine is #20,000 and the depreciation rate is 10% or 0.10.Plugging these values into the formula, we get:\[ \text{Value after 2 years} = 20000 \times (1 - 0.10)^2 \]\[ \text{Value after 2 years} = 20000 \times (0.9)^2 \]\[ \text{Value after 2 years} = 20000 \times 0.81 \]\[ \text{Value after 2 years} = 16200 \]Therefore, the value of the machine at the end of two years will be #16,200.