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Question
The difference between compound interest for a year payable half-yearly and simple interest on a certain sum of money lent out at 10% for a year is Rs. 15. Find the sum of money lent out.
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Solution
Let sum of money be Rs. y
To calculate S.I.
S.I. = `[ "P" xx "R" xx "T"]/100 = [ y xx 10 xx 1]/100 = Rs. y/10`
To calculate C.I.(compounded half-yearly)
∴ C.I. = P`[( 1 + r/[ 2 xx 100 ])^( n xx 2) - 1] = y[( 1 + 10/[ 2 x 100])^(1 xx 2) - 1 ]`
= `y[ (21/20)^2 - 1 ] = (41/400)y`
Given : C.I. - S.I. = Rs. 15
⇒ `(41/400)y - y/10 = 15`
⇒ `y/400 = 15 ⇒ y = Rs. 6,000.
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