A sum of money is invested at 20% compound interest (compounded annually). It would fetch Rs. 723 more in 2 years if interest is compounded half yearly. The sum is
Options:
A . Rs.7,500
B . Rs.15,000
C . Rs.20,000
D . Rs.30,000
Answer: Option D Answer: (d)Let the principal be Rs. x.When the interest is compounded annually,C.I. = P$[(1 + R/100)^T - 1]$= P$[(1 + 20/100)^2 - 1]$= P$[(6/5)^2 - 1]$= P$(36/25 - 1)$ = Rs.${11P}/25$When the interest is compounded half–yearly,C.I. = P$[(1 + 10/100)^4 - 1]$= P$[(11/10)^4 - 1]$= P$(14641/10000 - 1)$= Rs.${4641P}/10000$${4641P}/10000 - {11P}/25$ = 723${4641P - 4400P}/10000$ = 723${241P}/10000$ = 723P = ${723 × 10000}/241$ = Rs.30000
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