A sum of money was invested in a monetary fund for 2 years at the rate of compound interest of 20% per annum. If interest had been compounded at the interval of 6 months , then the compound interest would be Rs. 482 more of the same principal at the same rate of interest. Find the sum of money invested.

Explanation

Let the sum of the money invested be Rs. x
Then for the first case the amount of Rs.x after 2 years `=Rs.x xx (1+20/100)^(2)`
`=Rs.x xx(1+1/5)^(2)`
`5^(2)`
`=Rs.x xx(6/5)^(2)=Rs.(36x)/25`
Also for the second case, the amount of Rs. x after 2 years, the amount
`=Rs.x xx(1+(20/2)/100)^(2xx2)`
`=Rs. x xx(1+1/10)^(4)=Rs.x xx(11/10)^(4)`
As per question `(14641x)/10000-(36x)/25=482`
`implies(14641x-14400x)/10000=482`
`implies(241x)/1000-482`
`impliesx=(482xx10000)/241`
`impliesx=20000`
Hence Rs. 20000 was invested.