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Question
Simple interest on a sum of money for 2 years at 4% is Rs. 450. Find compound interest on the same sum and at the same rate for 1 year, if the interest is reckoned half yearly.
Solution
1st case
Given: S.I. = Rs. 450; Time = 2 years and Rate = 4%
∴ Principle = `[ "I" xx 100 ]/[ "R" xx "T"]`
= `[ 450 xx 100 ]/[ 4 xx 2 ]`
= Rs. 5625
2nd case (compounded half-yearly)
P = Rs. 5,625; n = 1 year and r = 4%
∴ A = P`(1 + r/[ 2 xx 100 ])^( n xx 2)`
= `5625(1 + 4/[ 2 xx 100 ])^(1 xx 2)`
= `5625(51/50)^2`
= Rs. 5852.25
∴ C.I. = 5852.25 - 5625
= Rs. 227.25
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