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Question
Find the difference between the compound interest compounded yearly and half-yearly for the following:
Rs 20,000 for `1 1/2` years at 16 % p.a.
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Solution
P=Rs 20,000; t = `1 1/2` years
When compounded yearly: r = 16% p.a.
`"A" = "P" (1 + "r"/100)^"n"`
A = Rs 20000 `(1 + 16/100)(1 + 16/100)^(1/2)`
= Rs 20000 × 1.16 × `(1 + 1/2 xx 16/100)`
= Rs 20, 000 x 1.16 x 1.08
= Rs 25,056
C.I. = A - P
= Rs (25,056 - 20,000)
= Rs 5,056
When compounded half-yearly:
`"A" = "P" (1 + "r"/100)^"n"`
A = Rs 20000 `(1 + 8/100)^3`
= Rs 20,000 x 1.08 x 1.08 x 1.08
= Rs 25,194.24
C.l. = A - P
= Rs (25,194.24- 20,000)
= Rs 5,194.24
Hence the difference in the interest=Rs (5,194.24 - 5,056) = Rs 138.24
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