Question

A certain sum of money is invested at rate of 10% per annum compound interest ,the interest compounded annually . If the difference between the interest of third year and first year is Rs. 1,105 , find the sum invested ​

Answer 1

For Annual compound intrest,Amount A at the end of n years is given by 
  A = P (1+r)^{n}P(1+r)n where, r is rate of intrest expressed as  percentage 

Rate of intrest on a amount C =c*r where r is rate of intrest expressed as  percentage
Let , the invested amount be P
rate of intrest r=10/100=0.1 

Intrest of first year = P * 10/100 = 0.1P
Amount at the end of second year = A2=P (1+0.1)^{2}P(1+0.1)2 
Intrest of third year = A2*0.1

Given , difference between intrest of third year and first year is rs.1105

So, 0.1*P*(1.1)^{2}(1.1)2   - 0.1P = 1105

0.1P(1.1^{2}-11.12−1 ) = 1105

0.1P(0.21) = 1105

P = Rs.52619