Question

The value of a machine costing Rs. $80000$ depreciates at the rate of $15\% $ per annum. What will be the worth of this machine after $3$ years?

Answer 1

Hint: Depreciation can be defined as the reduction in the value of an asset over the period of time. Here we will use the formula, $A = P{\left( {1 - \dfrac{r}{{100}}} \right)^n}$. Here negative sign is used for the condition being here is depreciation. Place the given values in the equation and simplify for the resultant required value.

Complete step by step solution:
Given that: The value of a machine costs, $P = Rs.80,000$
Rate of depreciation, $R = 15\% $
Number of years, $n = 3$years
Place all the given values in the equation –
$A = P{\left( {1 - \dfrac{r}{{100}}} \right)^n}$
$A = 80000{\left( {1 - \dfrac{{15}}{{100}}} \right)^3}$
Simplify the above the expression –
$A = 80000{\left( {1 - 0.15} \right)^3}$
$\Rightarrow A = 80000{\left( {0.85} \right)^3}$
$\Rightarrow A = 80000\left( {0.614125} \right)$
Simplify the above expression by finding the product of the terms.
$A = Rs.49130$.
Hence, the machine is worth $Rs.49130$ after three years.

Note:
> In simple words depreciation is particularly wear and tear and it leads to losses. It is the reduction in the recorded cost of the fixed asset and it may become zero or negligible over the period of years.

> Be wise enough to use the correct formula to solve these types of examples. The same formula can be used when the final price is given and we need to find out the initial price for the depreciating objects.