Question
On a certain sum of money, the difference between the compound interest for a year, payable half-yearly, and the simple interest for a year is 180. If the rate of interest in both the cases is 10%, then the sum is
Answer: Option D
Answer: (d)If the interest is compounded half yearly,C.I. = P$[(1 + R/100)^T - 1]$= P$[(1 + 5/100)^2 - 1]$= P$[(21/20)^2 - 1] = {41P}/400$S.I. = ${P × R × T}/100 = {P × 10}/100 = P/10$${41P}/400 - P/10$ = 180${41P - 40P}/400$ = 180$P/400 = 180$P = Rs.72000Using Rule 6,Here, C.I. - S.I. = Rs.180Interest is compounded half yearlyR = $10/5$ = 5%, T = 2 yearsC.I. - S.I. = P$(R/100)^2$180 = P$(5/100)^2$P = 180 × 20 × 20 ⇒ P = Rs.72000
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Answer: (d)If the interest is compounded half yearly,C.I. = P$[(1 + R/100)^T - 1]$= P$[(1 + 5/100)^2 - 1]$= P$[(21/20)^2 - 1] = {41P}/400$S.I. = ${P × R × T}/100 = {P × 10}/100 = P/10$${41P}/400 - P/10$ = 180${41P - 40P}/400$ = 180$P/400 = 180$P = Rs.72000Using Rule 6,Here, C.I. - S.I. = Rs.180Interest is compounded half yearlyR = $10/5$ = 5%, T = 2 yearsC.I. - S.I. = P$(R/100)^2$180 = P$(5/100)^2$P = 180 × 20 × 20 ⇒ P = Rs.72000
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