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Question
In what time will Rs. 1,500 yield Rs. 496.50 as compound interest at 20% per year compounded half-yearly ?
Solution
Given: P=Rs. 1,500; C.I.= Rs. 496.50 and r = 20%
Since interest is compounded semi-annually
Then, C.I. = `"P"[( 1 + r/[2 xx 100])^(n xx 2) - 1]`
⇒ 496.50 = 1,500`[( 1 + 20/[2 xx 100])^(n xx 2) - 1]`
⇒ `[496.50]/[1500] = (11/10)^(2n) - 1`
⇒ `331/1000 + 1 = (11/10)^(2n)`
⇒ `1331/1000 = (11/10)^(2n)`
⇒ `(11/10)^3 = (11/10)^(2n)`
On comparing, we get,
2n = 3 ⇒ n = `1 1/2` years
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