Difference between compounded interest and simple interest on a certain sum at 10% per annum for 2 years is Rs.52

Question

If difference between the compounded interest and the simple interest on a certain sum at 10% per annum for 2 years is Rs.52, then what would be the the sum?

Answer 1

Compound Interest - Simple Interest = Principle* { (1+(r/100))^n - (1+(r*n/100)) }

where 'r' is the rate of interest and n is the associated time period
here r=10;
CI - SI = 52;
and n=2;

So
CI-SI = Principle* { (1+(10/100))^2 - (1+(10*2/100)) }
52 = Principle*{ (11/10)^2 - (12/10) }
52 = Principle*{ (121/100) - (120/100) }
52 = Principle*(1/100)
Therefore Principle = Sum = 52*100 = 5200.

Answer 2

Let SUM = X
First we will calculate the amount of money we get at simple interest rate of 10% for 2 years
Amount of money to be : X x 0,1 x 2 = 0,2 X
Second, at compound interest rate
Amount of money to be : 0,1 X in the first year, (X + 0,1X) x 0,1 in the second year Total = 0,1X + 0,11X
Then I can write the following equation:
0,1 X + 0,11 X - 0,2 X = 52 or 0,01 X = 52
Therefore X = Rs 5200