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Question
Find the difference between compound interest and simple interest on Rs. 12,000 and in `1 1/2` years at 10% compounded half-yearly.
Solution
Given : P = Rs. 12,000 ; n = `1 1/2` years and r = 10%
S.I. = `[ P xx R xx T ]/100 = [12,000 xx 10 xx 3/2 ]/100 = Rs. 1,800`
To calculate C.I. ( Compound half - yearly ) :
P = Rs. 12,000; n = `1 1/2` years and r = 10%
A = `"P"( 1 + r/[ 2 xx 100 ])^(n xx 2)`
A = `12,000( 1 + 10/[ 2 xx 100 ])^(3/2 xx 2)`
A = `12,000( 21/20)^(3)`
A = Rs. 13,891.50
C.I. = Rs. 13,891.50 - Rs. 12,000 = Rs. 1,891.50
∴ Difference between C.I. and S.I = Rs. 1,891.50 - Rs. 1,800 = Rs. 91.50.
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