A man invests ₹ 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.
(a)₹ 5624.32
(b)₹ 5627.20
(c)₹ 5630.50
(d)₹ 5788.125
Answer
Answer (as printed): A
Explanation
C.I. earned during 1st year $=₹\left[5000\left(1+\frac{5}{100}\right)-5000\right]$ $$=₹(5250-5000)=₹ 250 \text {. }$$ Amount after 1st year $=₹(5250-20 \%$ of 250) $$=₹(5250-50)=₹ 5200 .$$ C.I. earned during 2nd year $=₹\left[5200\left(1+\frac{5}{100}\right)-5200\right]$ $$=₹(5460-5200)=₹ 260 .$$ Amount after 2nd year $=₹(5460-20 \%$ of 260) $$=₹(5460-52)=₹ 5408 .$$ C.I. earned during 3rd year $=₹\left[5408\left(1+\frac{5}{100}\right)-5408\right]$ $$=₹(5678.40-5408)=₹ 270.40 .$$ Amount after 3rd year $=₹(5678.40-20 \%$ of 270.40 $)$ $$=₹(5678.40-54.08)=₹ 5624.32 \text {. }$$
Explanation as extracted from the printed page; notation may be imperfect.