Question

A washing machine was bought as \[Rs.{\text{ }}15,625\] three years ago, if its value
depreciates at 16% p.a., calculate
(iii) Its present value;
(iv) Its value after one year from now.

Answer 1

Hint: Find the present value of the washing machine using the formula given below:
Present value$ = {\text{Cost price}}{\left( {1 - \dfrac{{{\text{rate per annum}}}}{{100}}}
\right)^t}$
Substitute the values and get the desired result.

It is given that three years ago, a washing machine was bought\[Rs.{\text{ }}15,625\]. It is also
given that its value depreciates at 16% p.a.
We have to find the present value of the washing machine and its value after one year from now.
We have given, the cost price three years ago, the rate of depreciation and the time as:
Cost price$ = Rs.15,625$
Rate per annum$ = 16\% $ p.a.
Time$ = 3$years
Then the present value of the washing machine can be given as:
Present value$ = {\text{Cost price}}{\left( {1 - \dfrac{{{\text{rate per annum}}}}{{100}}}
\right)^t}$
Substitute the values of the cost price three years ago, the rate of depreciation and the time so we
have the present value as:
Present value$ = 15625{\left( {1 - \dfrac{{{\text{16}}}}{{100}}} \right)^3}$
Present value$ = 15625{\left( {\dfrac{{84}}{{100}}} \right)^3}$
Present value$ = 15625{\left( {\dfrac{{21}}{{25}}} \right)^3}$
Present value$ = 15625\left( {\dfrac{{21 \times 21 \times 21}}{{25 \times 25 \times 25}}}
\right)$
Present value$ = 9261$

Therefore, the present value of the washing machine is Rs.$9261$.

Now, the present cost price of the washing machine is Rs.$9261$, so the value of the washing
machine after the one year is given as:
Value of Machine after one year$ = 9261{\left( {1 - \dfrac{{16}}{{100}}} \right)^1}$
Value of Machine after one year$ = 9261\left( {\dfrac{{84}}{{100}}} \right)$
Value of Machine after one year$ = 9261\left( {\dfrac{{21}}{{25}}} \right)$
Value of Machine after one year$ = 7779.24$
Therefore, the value of the washing machine after one year is Rs.$7779.24$.

Note: When we find the value of the machine after one year from now, we use the cost price of
the washing machine at the present time that was obtained in the part (i).