Question

# A new car costs Rs. 360000. Its price depreciates at the rate of 10% a year during the first two years and the rate of 20% a year thereafter. What will be the price of the car after 3 years?

Hint: We cannot calculate directly the cost of the car after three years. We need to calculate the price every year. We need to find the depreciation of the car according to the condition given and subtract from the previous price to get the new price of the car. The formula for depreciation as follows $\text{Depreciation = percentage }\!\!\times\!\!\text{ cost price}$ .

We need to find the cost of the car after three years after applying certain conditions.
Let's start by finding the cost of the car after the first year.
According to the condition the cost of the car reduces by 10% during the first two years each, this means that there is a drop of 10% of the price of the car at the end of the first year.
Calculating 10% of the cost price we get,
$\text{Depreciation = }\dfrac{\text{10}}{\text{100}}\text{ }\!\!\times\!\!\text{ cost price}............\text{(i)}$
Substituting the value of the car, we get,
$\text{Depreciation = }\dfrac{\text{10}}{\text{100}}\text{ }\!\!\times\!\!\text{ 360000}$ .
Solving for the depreciation, we get,
$\text{Depreciation = }\dfrac{10}{100}\times \text{360000 = Rs 36000}$ .
Therefore the price of the car after the first year is the original price – depreciation price.
By substituting the values we get,
Price after first year = 360000 – 36000 = Rs. 324000…………..(ii)
Now let's find the price after the second year.
According to the condition the cost of the car reduces by 10% during the first two years each, this means that there is a drop of 10% of the price of the car at the end of the second year.
Calculating 10% of the cost price we get,
$\text{Depreciation = }\dfrac{\text{10}}{\text{100}}\text{ }\!\!\times\!\!\text{ cost price}$ .
Substituting the value of the car after the first year, we get,
$\text{Depreciation = }\dfrac{\text{10}}{\text{100}}\text{ }\!\!\times\!\!\text{ 324000}$ .
Solving for the depreciation, we get,
$\text{Depreciation = }\dfrac{10}{100}\times \text{324000 = Rs 32400}$ .
Therefore the price of the car after the first year is the original price – depreciation price.
By substituting the values we get,
Price after first year = 324000 – 32400 = Rs. 291600…………..(iii)
Now let's find the price after the third year,
According to the condition the cost of the car reduces by 20% after the first two years, this means that there is a drop of 20% of the price of the car at the end of the third year.
Calculating 20% of the cost price we get,
$\text{Depreciation = }\dfrac{\text{20}}{\text{100}}\text{ }\!\!\times\!\!\text{ cost price}$ .
Substituting the value of the car after the first year, we get,
$\text{Depreciation = }\dfrac{\text{20}}{\text{100}}\text{ }\!\!\times\!\!\text{ 291600}$ .
Solving for the depreciation, we get,
$\text{Depreciation = }\dfrac{20}{100}\times 291600\text{ = Rs 58320}$ .
Therefore, the price of the car after the first year is the original price – depreciation price.
By substituting the values, we get,
Price after first year = 291600 – 58320 = Rs. 233280…………..(iv)
Therefore, the price of the car after the third year is Rs. 233280.

Note: We need to keep in mind that after every year the price of the car is changing therefore even if depreciation percentage is the same in the first two years the cost of depreciation will change. The depreciation cost for the second time will be calculated with respect to the new cost of the car. Also, we have to keep in mind that we need to subtract the depreciation cost from the previous cost of the car in order to get the new cost of the car.