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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.
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Solution
Given: P = Rs. 10,000 ; n = 18 months = `1 1/2` year and r = 10% p.a.
For First year
I = `(10,000xx10xx1)/100`
= 1,000
A = 10,000 + 1,000
= 11,000
For Second year,
P = 11,000, r = 10%, n = `1/2` year
I = `(11,000xx10xx1/2)/100`
= 550
A2 = 11,000 + 550
= 11,550
C.I. = A – P
= 11,550 – 10,000
= 1,550
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
Compound interest yearly = 11576.25 – 10,000
= 1576.25
Therefore, the difference between both C.I
= 1576.25 – 1,550
= 26.25
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