Question

The cost of a machine depreciates by 10% every year. Its present worth is rs.18000. What will be its value after 3 years

Answer 1

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Answer 2

The value of the machine after 3 years = Rs. 13122

Given :

• The cost of a machine depreciates by 10% every year.

• The present worth is Rs. 18000

To find :

The value of the machine after 3 years

Solution :

Step 1 of 2 :

Write down the present value and rate of decrease

Here it is given that the cost of a machine depreciates by 10% every year.

The present worth is Rs. 18000

Step 2 of 2 :

Find value of the machine after 3 years

So by the given

Present value = P = Rs. 18000

Time = n = 3 years

Rate of decrease per year = r % = 10%

Hence the value of the machine after 3 years

$\displaystyle \sf{ =P {\bigg(1 - \frac{r}{100} \bigg)}^{n} }$

$\displaystyle \sf{ =Rs. \: 18000 \times {\bigg(1 - \frac{10}{100} \bigg)}^{3} }$

$\displaystyle \sf{ =Rs. \: 18000 \times {\bigg( \frac{100 - 10}{100} \bigg)}^{3} }$

$\displaystyle \sf{ =Rs. \: 18000 \times {\bigg( \frac{90}{100} \bigg)}^{3} }$

$\displaystyle \sf{ =Rs. \: 18000 \times {\bigg( \frac{9}{10} \bigg)}^{3} }$

$\displaystyle \sf{ =Rs. \: 18000 \times \frac{9}{10} \times \frac{9}{10} \times \frac{9}{10} }$

$\displaystyle \sf{ =Rs. \: 13122 }$

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