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Question
Find the difference betlween the compound interest compounded yearly and half-yearly for the following:
Rs 15,000 for `1 1/2` years at 12 % p.a.
Solution
P=Rs 15,000 ; t = `1 1/2` years
When compounded yearly : r = 12 % p.a.
`"A" = "P" (1 + "r"/100)^"n"`
A = Rs `15000 (1 + 12/100)(1 + 12/100)^(1/2)`
= Rs 15000 x 1.12 x `(1 + 1/2 xx 12/100)`
= Rs15,000 x 1.12 x 1.06
= Rs 17,808
C.l. = A - P
= Rs (17,808 -15,000)
= Rs 2808
When compounded half-yearly :
`"A" = "P" (1 + "r"/100)^"n"`
A = Rs 15000 `(1 + 6/100)^3`
= Rs 15,000 x 1.06 x 1.06 x 1.06
= Rs 17,865.24
C.l. = A - P
= Rs (17,865.24 - 15,000)
= Rs2,865.24
Hence the difference in the interest=Rs (2,865.24 - 2,808) =Rs 57.24
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