A man invests Rs. 5000 for 3 years at 5% p.a. compound interest reckoned yearly. Income tax at the rate of 20% on the interest earned is deducted at the end of each year. Find the amount at the end of the third year = ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{C}}{\text{.I}}{\text{. earned during }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr & {\text{= }}\,{\text{Rs}}{\text{.}}\left[ {5000\left( {1 + \frac{5}{{100}}} \right) - 5000} \right]{\text{ }} \cr & = {\text{Rs}}{\text{. }}\left( {5250 - 5000} \right) \cr & = {\text{Rs}}{\text{. 250}} \cr & {\text{Amount after }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr & = {\text{Rs}}{\text{. }}\left( {5250 - 20\% {\text{ of }}250} \right) \cr & = {\text{Rs}}{\text{.}}\left( {5250 - 50} \right){\text{ }} \cr & {\text{= }}\,{\text{Rs}}{\text{.}}\,{\text{5200 }} \cr & {\text{C}}{\text{.I}}{\text{. earned during }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr & = {\text{Rs}}{\text{.}}\left[ {5200\left( {1 + \frac{5}{{100}}} \right) - 5200} \right]{\text{ }} \cr & = {\text{Rs}}{\text{. }}\left( {5460 - 5200} \right) \cr & = {\text{Rs}}{\text{.260 }} \cr & {\text{Amount after }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} \cr & {\text{= Rs}}{\text{. }}\left( {5460 - 20\% {\text{ of }}260} \right) \cr & {\text{= Rs}}{\text{. }}\left( {5460 - 52} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{5408 }} \cr & {\text{C}}{\text{.I}}{\text{. earned during }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr & {\text{= Rs}}{\text{. }}\left[ {5408\left( {1 + \frac{5}{{100}}} \right) - 5408} \right] \cr & = {\text{Rs}}{\text{. }}\left( {5678.40 - 5408} \right) \cr & = {\text{Rs}}{\text{.}}\,{\text{270}}{\text{.40 }} \cr & {\text{Amount after }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} \cr & = {\text{Rs}}{\text{. }}\left( {5678.40 - 20\% \,{\text{of }}270.40} \right) \cr & = {\text{Rs}}{\text{. }}\left( {5678.40 - 54.08} \right) \cr & = {\text{Rs}}{\text{. 5624}}{\text{.32}} \cr} $$