Question

Value of machine depreciates every year at 15%. If its present value is Ks. 480000, what will be its value after 3 years?​

Answer 1

Question :-

Value of machine depreciates every year at 15%. If its present value is Rs. 480000, what will be its value after 3 years?

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

Given that,

Present value of car, P = Rs 480000

Rate of depreciation, r = 15 % per annum.

Time, n = 3 years

We know,

The depreciated value ( DV, ) received on a certain sum of value depreciated at the rate of r % per annum in n years is given by

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

So, on substituting the values, we get

$\rm\:DV \: = \: 480000 \: {\bigg[1 - \dfrac{15}{100} \bigg]}^{3} \:$

$\rm\:DV \: = \: 480000 \: {\bigg[ \dfrac{100 - 15}{100} \bigg]}^{3} \:$

$\rm\:DV \: = \: 480000 \: {\bigg[ \dfrac{85}{100} \bigg]}^{3} \:$

$\rm\:DV \: = \: 480000 \: {\bigg[ \dfrac{17}{20} \bigg]}^{3} \:$

$\rm\implies \:DV \: = \: Rs \: 294780$

So, Value of machine depreciates at the rate of 15%, if its present value is Rs. 480000, then its value after 3 years is Rs 294780.

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

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 6 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

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

Answer 2

PROVIDED INFORMATION :-

Value of machine depreciates every year at 15%. If its present value is rs. 480000

QUESTION :-

Value of machine depreciates every year at 15%. If its present value is rs. 480000, what will be its value after 3 years?

TO FIND :-

what will be its value after 3 years = ?

SOLUTION :-

Present cost of machine = rs 480000

Required cost of machine after 3 years

= 480000 { 1 - 15/100} 3

480000 × 17/20 × 17/20 × 17/20

= rs 294780

value after 3 years = rs 294780