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The difference between the compound interest and the simple interest on a certain sum at 10 % per annum for 2 years is Rs 52 . Find the sum. [ Calculator, Method and examples ]

Solution:
Your problem `->` The difference between the compound interest and the simple interest on a certain sum at 10 % per annum for 2 years is Rs 52 . Find the sum.


Here `R = 10 %, N = 2` years and `CI - SI = 52` .

Let the sum be Rs. `X`. Then,

`SI = (P*R*N)/100 = (X * 10 * 2) / 100 = 0.2 X`

`CI = P (1 + R/100)^N - P`

`= X ( 1 + 10 / 100 ) ^ 2 - X`

`= X ( 110 / 100 ) ^ 2 - X`

`= X (( 110 / 100 ) ^ 2 - 1 )`

`= 0.21 X`


`:. CI - SI = 0.21 X - 0.2 X = 0.01 X`

So, `0.01 X = 52`

=>` X = 5200` .

Hence, Sum = Rs. `5200`.






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