Question

. Paramveer purchased a car for 4,00,000. If the total cost of the car is depreciating at the rate of 10% p.a., calculate its value after 3 years. ​

Answer 1

Answer:

= 4,00,000(1-10/100)³

= 4,00,000(90/100)³

= 2,91,600

Hence, price after 3 years = ₹2,91,600

Step-by-step explanation:

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Answer 2

$\large\underline{\sf{Solution-}}$

Given that,

Paramveer purchased a car for 4,00,000. The total cost of the car is depreciating at the rate of 10% p.a

So, we have

Present value of car, P = 400000

Rate of depreciation, r = 10 % per annum

Time period, n = 3 years

We know,

Amount received on a certain sum of money of Rs P depreciated at the rate of r % per annum for n years is given by

$\boxed{\rm{  \:Amount \: = \: P {\bigg[1 - \dfrac{r}{100} \bigg]}^{n} \: \: }}$

So, on substituting the values, we get

$\rm \: Amount = 400000 {\bigg[1 - \dfrac{10}{100} \bigg]}^{3}$

$\rm \: Amount = 400000 {\bigg[1 - \dfrac{1}{10} \bigg]}^{3}$

$\rm \: Amount = 400000 {\bigg[ \dfrac{10 - 1}{10} \bigg]}^{3}$

$\rm \: Amount = 400000 {\bigg[ \dfrac{9}{10} \bigg]}^{3}$

$\rm \: Amount = 400000 \times \frac{729}{1000}$

$\rm \: Amount = 400 \times 729$

$\rm\implies \:\boxed{\rm{  \:Amount \: = \: 291600 \: \: }}$

So, The amount of car after 3 years be 2, 91, 600.

$\rule{190pt}{2pt}$

Additional Information :-

1. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded annually for n years is given by

$\boxed{\rm{  \:Amount \: = \: P {\bigg[1 + \dfrac{r}{100} \bigg]}^{n} \: \: }}$

2. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded semi - annually for n years is given by

$\boxed{\rm{  \:Amount \: = \: P {\bigg[1 + \dfrac{r}{200} \bigg]}^{2n} \: \: }}$

3. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded quarterly for n years is given by

$\boxed{\rm{  \:Amount \: = \: P {\bigg[1 + \dfrac{r}{400} \bigg]}^{4n} \: \: }}$

4. Amount received on a certain sum of money of Rs P invested at the rate of r % per annum compounded monthly for n years is given by

$\boxed{\rm{  \:Amount \: = \: P {\bigg[1 + \dfrac{r}{1200} \bigg]}^{12n} \: \: }}$