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Question
Find the difference between the compound interest compounded yearly and half-yearly on Rs. 10,000 for 18 months at 10% per annum.
Solution
(i) When interest is compounded yearly :
Given : P = Rs. 10,000 ; n = 18 months = `1 1/2` year and r = 10% p.a.
For 1 year
A = `"P"( 1 + r/100)^n (1 + r/200)^(1/cancel2) xxcancel2`
= `10,000 xx 11/ 10 xx 21/ 20`
= 1020 × 11
= 11,550
When interest is compounded half-yearly
`A = P (1 + r/200)^(nxx2)`
= `10,000 (1 + 10/200)^(3/cancel2 xxcancel2`
=`10,000 xx 21/20 xx 21/20 xx 21/20`
= `(105 xx 441)/4`
= `46305/4`
= 11576.25
Therefore, the difference between both C.I
₹11,576.25 - ₹11,550
= ₹26.25
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