Question

The cost of a refrigerator is 9000. Its value depreciates at a rate of 5% every year. Find the total depreciation at the end of 2 years.

Answer 1

Hint: We solve this problem by using the percentages. The formula of depreciation having the principal value \['P'\] and rate of depreciation as \['R'\] is given as
\[\text{depreciation}=P\times \dfrac{R}{100}\]
Then we use the formula that is the amount after the depreciation is given as
\[\text{Amount}=P-\text{Depreciation}\]
By using the depreciation in two years we get total depreciation by adding the two depreciations.

Complete step by step answer:
We are given that the cost of refrigerator as 9000
Let us assume that this cost as principal value that is
\[\Rightarrow P=9000\]
We are given that the cost deprecates at a rate of 5% every year.
Let us assume the rate of depreciation as
\[\Rightarrow R=5%\]
Now, let us find the depreciations of first year
(i) We know that the principal value for first year as
\[\Rightarrow P=9000\]
Let us assume that the depreciation for first year as \['{{D}_{1}}'\]
We know that the formula of depreciation having the principal value \['P'\] and rate of depreciation as \['R'\] is given as
\[\text{depreciation}=P\times \dfrac{R}{100}\]
Now, by using the above formula we get
\[\begin{align}
  & \Rightarrow {{D}_{1}}=9000\times \dfrac{5}{100} \\
 & \Rightarrow {{D}_{1}}=450 \\
\end{align}\]
We know that the amount after the depreciation is given as
\[\text{Amount}=P-\text{Depreciation}\]
By using the above formula we get the amount after first year as
\[\begin{align}
  & \Rightarrow A=9000-450 \\
 & \Rightarrow A=8550 \\
\end{align}\]
Now, let us find the depreciation in second year.
(ii) We know that the amount after the depreciation of first year will be the principal value for second year because the rate of depreciation is given for every year.
So, we can say that the principal value for second year is \['A'\]
Let us assume that the depreciation for first year as \['{{D}_{2}}'\]
Now by using the depreciation formula we get
\[\Rightarrow {{D}_{2}}=A\times \dfrac{R}{100}\]
By substituting the required values in above equation we get
\[\begin{align}
  & \Rightarrow {{D}_{2}}=8550\times \dfrac{5}{100} \\
 & \Rightarrow {{D}_{2}}=427.5 \\
\end{align}\]
Now, let us assume that the total depreciation at the end of 2 years as \[D\] then we get
\[\begin{align}
  & \Rightarrow D={{D}_{1}}+{{D}_{2}} \\
 & \Rightarrow D=450+427.5 \\
 & \Rightarrow D=877.5 \\
\end{align}\]

Therefore, we can say that the total depreciation of refrigerator at the end of 2 years is 877.5

Note: Students may make mistakes in calculating the depreciation of the second year.
We are given that the rate of depreciation is 5% for every year.
This means that the amount after the depreciation of the first year will be the principal value for the second year. Then we get the depreciation of second year as
\[\Rightarrow {{D}_{2}}=A\times \dfrac{R}{100}\]
But students may do mistake and take the formula as
\[\Rightarrow {{D}_{2}}=P\times \dfrac{R}{100}\]
This gave the wrong answer because the rate of depreciation will be with respect to principal value at the start of the year.
So, the principal value at the start of second year will be the amount at the end of first year.