Question

The value of a machine depreciates (decreases) every year by 5% If the present value of the machine is 24000, what will be the value of the machine after 2 years?

Answer 1

Initial value of machine =24000

5% decreased in first year =24000−24000×5÷100=22800

Again, 5% decreased in second year =22800−22800×5÷100=21660

Answer 2

Answer:

Given :-

• The value of a machine depreciates (decreases) every year by 5%.
• The present value of the machine is Rs 24000.

To Find :-

• What is the value of machine after 2 years.

Formula Used :-

$\longmapsto \sf\boxed{\bold{\pink{A =\: P\bigg(1 - \dfrac{r}{100}\bigg)^n}}}$

where,

• A = Amount
• P = Principal
• r = Rate of Interest
• n = Time

Solution :-

Given :

$\bigstar$ Principal (P) = Rs 24000

$\bigstar$ Rate of Interest (r) = 5%

$\bigstar$ Time (n) = 2 years

According to the question by using the formula we get,

$\longrightarrow \sf A =\: 24000\bigg(1 - \dfrac{5}{100}\bigg)^2$

$\longrightarrow \sf A =\: 24000\bigg(\dfrac{100 - 5}{100}\bigg)^2$

$\longrightarrow \sf A =\: 24000\bigg(\dfrac{95}{100}\bigg)^2$

$\longrightarrow \sf A =\: 24{\cancel{0}}{\cancel{00}} \times \dfrac{95}{10\cancel{0}} \times \dfrac{95}{1\cancel{00}}$

$\longrightarrow \sf A =\: \dfrac{24 \times 95 \times 95}{10}$

$\longrightarrow\sf A =\: \dfrac{21660\cancel{0}}{1\cancel{0}}$

$\longrightarrow \sf A =\: \dfrac{21660}{1}$

$\longrightarrow \sf\bold{\red{A =\: Rs\: 21660}}$

$\therefore$ The value of the machine after 2 years is Rs 21660.