Question

Find the value of an air conditioner after \[2\]years, if its price is \[Rs.3000\] and it depreciates by \[10\% \] per month?

Answer 1

Hint: First, we shall analyze the given information so that we can easily calculate the desired answer.
In the question, we are given the new price of an air conditioner (present). The air conditioner price has been decreasing (depreciation) each month \[10\% \]. By using the amount formula, we can easily find the price of an air conditioner after \[2\] years.
Formula to be used:
The formula used to calculate the amount is
 Amount, \[A{\text{ = }}P\left[ {{{\left( {1 - \;\dfrac{r}{{100}}} \right)}^n}} \right]\]
Where, $P$ is the principal amount, $r$ denotes the rate of interest in years and $n$ denotes the number of years.

Complete step by step answer:
It is given that, the principal amount, \[P = 3000\], the rate of interest (In years), \[r = 10\% \] and the number of years, \[n = 2\]years.
To find The amount of air conditioner after \[2\] years.
Now, we shall substitute the given values in the formula.
Amount, \[A{\text{ = }}P\left[ {{{\left( {1 - \;\dfrac{r}{{100}}} \right)}^n}} \right]\] where, $P$ is the principal amount, $r$ denotes the rate of interest in years and $n$ denotes the number of years.
That is \[A{\text{ = 3000}}\left[ {{{\left( {1 - \;\dfrac{{10}}{{100}}} \right)}^2}} \right]\]
We shall take LCM for the numbers inside the brackets.
\[A{\text{ = 3000}}\left[ {{{\left( {\;\dfrac{{100 - 10}}{{100}}} \right)}^2}} \right]\]
\[{\text{ = 3000}}\left[ {{{\left( {\;\dfrac{{90}}{{100}}} \right)}^2}} \right]\]
\[{\text{ = 3000}}\left[ {{{\left( {\;\dfrac{9}{{10}}} \right)}^2}} \right]\]
\[{\text{ = 3000}} \times \dfrac{9}{{10}} \times \dfrac{9}{{10}}\]
\[{\text{ = 30}} \times 9 \times 9\]
$ = 2430$
Hence, $A = Rs.2430$
Therefore, the amount of air conditioner after \[2\] years is $A = Rs.2430$ .

Note: In this question, the principal, rate of interest, and the no. of years are given. So directly by applying the amount formula and substituting the value, we can get the answer. The principal amount is the amount that is being sold at present. So, the amount is being depreciated (lowered) \[10\% \] per month. Depreciation is the hint word from the question; we can conclude that the amount will be lesser than the present amount.