Question

The initial cost of the TV is 64000 the TV was depreciated for the first two years at rate of 5% than it becomes 8%for the n XT two years and than it becomes 10% for the fifth year find the depreciated value of the TV for five years

Answer 1

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

Given that

$\: \: \: \: \: \bull \: \: \: \sf{ Cost\:_{(TV)}=Rs \: 64000}$

$\: \: \: \: \: \bull \: \: \:\sf{ Rate \: of \: depreciation\:_{(r_1)}=5\%}$

$\: \: \: \: \: \bull \: \: \:\sf{ Time\:_{(t_1)}=2\: year}$

$\: \: \: \: \: \bull \: \: \:\sf{ Rate \: of \: depreciation\:_{(r_2)}=8\%}$

$\: \: \: \: \: \bull \: \: \:\sf{ Time\:_{(t_2)}=2\: year}$

$\: \: \: \: \: \bull \: \: \:\sf{ Rate \: of \: depreciation\:_{(r_3)}=10\%}$

$\: \: \: \: \: \bull \: \: \:\sf{ Time\:_{(t_3)}=1\: year}$

We know,

☆ If a certain sum of money P is depreciated for successive rate of interest, then amount A is given by

$\rm :\longmapsto\:A = P {\bigg(1 - \dfrac{r_1}{100} \bigg) }^{t_1}{\bigg(1 - \dfrac{r_2}{100} \bigg) }^{t_2}{\bigg(1 - \dfrac{r_3}{100} \bigg) }^{t_3}$

☆ On substituting the values, we get

$\rm :\longmapsto\:A = 64000{\bigg(1 - \dfrac{5}{100}\bigg) }^{2}{\bigg(1 - \dfrac{8}{100}\bigg) }^{2}{\bigg(1 - \dfrac{10}{100}\bigg) }^{1}$

$\rm :\longmapsto\:A = 64000 {(0.95)}^{2} {(0.92)}^{2}(0.9)$

$\bf\implies \:A = 43999.25$

Hence,

• Price of TV after 5 years will be Rs 43999.25

Additional Information :-

If a certain sum of money Rs P is invested at the rate of r % per annum compounded annually for the time period of n years, then Amount is

$\boxed{ \sf \: A = P{\bigg(1 + \dfrac{r}{100} \bigg) }^{n}}$

☆ If a certain sum of money Rs P is invested at the rate of r % per annum compounded half yearly for the time period of n years, then Amount is

$\boxed{ \sf \: A = P{\bigg(1 + \dfrac{r}{200} \bigg) }^{2n}}$

☆ If a certain sum of money Rs P is invested at the rate of r % per annum compounded quarterly for the time period of n years, then Amount is

$\boxed{ \sf \: A = P{\bigg(1 + \dfrac{r}{400} \bigg) }^{4n}}$