Find the sum of money if the difference between compound interest and simple interest for 2 years at the rate of 9% interest per annum is Rs. 129.60

Explanation

Let the sum of money be Rs. x.
`:.` At the rate of 9% interest per annum the amount of Rs.x for 2 years `=Rs. (1+9/100)^(2)`
`:.` The compound interet `=Rs. {x(1+9/100)^(2)-x}=Rs. X{(1+9/100)^(2)-1}`
`=Rs. X{(1+9/100)^(2)-(10^(2))=Rs. X{(1+9/100+1)(1+9/100-1)}`
`=Rs.x(2+9/100)xx9/100=Rs. x xx209/100xx+9/100`
`=Rs. (1881x)/10000`
Again at the rate of 9% interest per annum.
the simple of interest of Rs. x for 2 years `=Rs. (x xx9xx2)/100`
`=Rs. (9x)/50`
As per question `(1881x)/10000-(9x)/50=129.60`
`implies(1881x-1800x)/10000=129.60`
`implies81x=1296000`
`impliesx=1296000/81=16000`
`:.`The required sum of money `=Rs. 16000`