Question

A company purchases an office copier machine for Rs. 50,000. It is estimated that the copier depreciates in its value at a rate of 15% per year. What will be the value of the copier after 15 years?

Answer 1

Hint: The initial value of the copier machine is Rs. 50,000. The rate of depreciation of the copier machine is 15% and the time for depreciation is 15 years. Now, use the formula, \[\text{Net value of the machine=Initial value}{{\left( \text{1-}\dfrac{\text{rate}}{\text{100}} \right)}^{\text{time}}}\] and calculate the net value of the copier machine after 15 years.

Complete step-by-step answer:
It is given that a company purchases an office copier machine for Rs. 50,000. It is estimated that the copier depreciates in its value at a rate of 15% per year.
The price of the copier machine that is the initial value of the copier machine = Rs. 50,000 ……………………………………(1)
The rate of depreciation of copier machine per year = 15% …………………………………..(2)
The time for depreciation = 15 years …………………………………………(3)
For the first year the copier machine reduces its value by 15%. For the next year the copier machine reduces its value by 15% of the remaining worth again. So, we can say that the net worth is of the form of the amount in compound interest. The only difference is that while calculating the amount for compound interest, we add the interest and here, we are deducting the depreciated amount from the initial worth. Like,
\[\text{Net value of the machine=Initial value}{{\left( \text{1-}\dfrac{\text{rate}}{\text{100}} \right)}^{\text{time}}}\] …………………………………(4)
 From equation (1), equation (2), and equation (3), we have the initial value of the copier machine, the rate of depreciation and the time of depreciation respectively.
Now, from equation (1), equation (2), equation (3) and equation (4), we get
\[\text{Net value of the machine=Rs}\text{. 50000}{{\left( \text{1-}\dfrac{15}{\text{100}} \right)}^{15}}=\text{Rs}\text{. 50000}{{\left( \dfrac{85}{100} \right)}^{15}}=\text{Rs}\text{. 50000}{{\left( 0.85 \right)}^{15}}\]
\[=\text{Rs}\text{.50000}\times \text{0}\text{.087354=Rs}\text{. 4367}\text{.71}\] …………………………….(5)
Hence, the value of the copier after 15 years is Rs. 4367.71.

Note: In this question, one might think that depreciation means adding value to something and then use the formula, \[\text{Net value of the machine=Initial value}{{\left( \text{1+}\dfrac{\text{rate}}{\text{100}} \right)}^{\text{time}}}\] to get the net value of the copier machine after 15 years. We cannot use this formula here because depreciation means reduction of value of something with time. So, we have use the formula, \[\text{Net value of the machine=Initial value}{{\left( \text{1-}\dfrac{\text{rate}}{\text{100}} \right)}^{\text{time}}}\].