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Question
Find the difference between the simple interest and compound interest on 2,500 for 2 years at 4% p.a., compound interest being reckoned semi-annualy.
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Solution
P = ₹ 2,500
r = 4% p.a. = `(4)/(2)` = 2% half yearly
T = 2 year = 4 half years
A = P`(1 + r/100)^n`
= ₹ 2,500 `(1 + 2/100)^4`
= ₹ 2,500 `(1 + 1/50)^4`
= ₹ 2,500 `((51)/(50))^4`
= ₹`(2,500 xx 51 xx 51 xx 51 xx 51)/(50 xx 50 xx 50 xx 50)`
= ₹ `(51 xx 51 xx 51 xx 51)/(50 xx 50)`
= ₹ `(2,601 xx 2,601)/(2,500)`
= ₹`(67,65,201)/(2,500)`
= ₹ 2,706·08
C.I. = A - P
= ₹ (2,706·08 - ₹ 2,500)
= ₹ 206·08
and S.I. = `"PRT"/(100) = ₹ (2,500 xx 4 xx 2)/(100)` = ₹ 200
Difference between C.I. and S.I.
= C.I. - S.I.
= ₹ 206·08 - ₹ 200
= ₹ 6·08.
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