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Question
A sum of money is invested at 10% per annum compounded half yearly. If the difference of amounts at the end of 6 months and 12 months is Rs.189, find the sum of money invested.
Solution
Let the sum of money be Rs. y
and rate = 10% p.a. compounded half yearly
For first 6 months
∴ A = P`( 1 + r/[ 2 xx 100])^( n xx 2) = y( 1 + 10/2 xx 100)^(1/2 xx 2) = (21/20)y`
For first 12 months
∴ A = P`( 1 + r/[ 2 xx 100])^( n xx 2) = y( 1 + 10/2 xx 100)^(1 xx 2) = (441/400)y`
Given: The difference between the above amounts = Rs.189
⇒ `( 441/400)y - (21/20)y = 189`
⇒ ` (21/400)y = 189`
⇒ ` y = [189 xx 400]/21`
y = 3600.
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