Question

The valuble is a machine decreases every year by 5%. If the present value of the machine is rupees 24,000,what will be the value of machine after 2years?​

Answer 1

✬ Value = Rs 21660 ✬

Step-by-step explanation:

Given:

• Present value of machine is Rs 24000.
• Value decreases by 5 % every year.

To Find:

• What will be the value of machine after 2 years ?

Solution: Here we have

• P = 24000
• R = 5 %
• T = 2 years

This forms compound interest. Since this is decreasing so formula will be

★ A = P × (1 – r/100)ⁿ ★

$\implies{\rm }$ A = 24000 × (1 – 5/100)²

$\implies{\rm }$ 24000 × (100 – 5/100)²

$\implies{\rm }$ 24000 × (95/100)²

$\implies{\rm }$ 24000 × 9025/10000

$\implies{\rm }$ 24 × 9025/10

$\implies{\rm }$ 216600/10

$\implies{\rm }$ 21660

Hence , value of machine after 2 years will be Rs 21660.

[ Another method ]

• Value decreases by 5 % every year.

➨ In first year it will decrease by 5% of 24000

➨ 1st year = 5/100 × 24000

➨ 120000/100 = 1200

Value = 24000 – 1200 = 22800

➨ In 2nd year it will decrease by 5% of 22800

➨ 2nd year = 5/100 × 22800

➨ 114000/100 = 1140

Value = 22800 – 1140 = 21660

Hence , value of machine after 2 years will be Rs 21660.

Answer 2

Answer:

• Present Value = Rs. 24,000
• Decrease Every Year = 5%
• Value after 2 years?

$\underline{\bigstar\:\textsf{According to the given Question :}}$

Let the Depreciation in 1st Year be 5% Hence it will be (5 × 2)% = 10% in 2 year.

$:\implies\sf Value=Total-\bigg(Total \times 10\%\bigg)\\\\\\:\implies\sf Value=24000-\bigg(24000 \times \dfrac{10}{100} \bigg)\\\\\\:\implies\sf Value=24000-\bigg(2400 \times 10\bigg)\\\\\\:\implies\sf Value = 24000 - 2400\\\\\\:\implies\underline{\boxed{\sf Value = Rs. \:21600}}$

⠀

$\therefore\:\underline{\textsf{Value of machine after 2 year is \textbf{Rs. 21,600}}}.$