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.

Answer 1

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.