Question

The difference between the compound interest and simple interest on a certain sum of money for 2 years at 10% per annum is Rs 15. find the sum of money

Answer 1

CI = P[1+r/100]^n-P

 

SI = pnr/100

 

From the problem,

 

R = 10%

N = 2

CI – SI = 15

 

We need to find p.

 

CI – SI = P[1+r/100]^n-P-Pnr/100

 

=P[(1+r/100)^n-1-nr/100]

 

Substituting the values of n and r, we get

 

CI – SI = 15 = P[1+10/100)^2-1-20/100]

 

Let us consider the expression within the square brackets.

 

Expanding and subtracting the remaining values, we get

 

1+20/100+100/10000-1-20/100 = 100/10000 = 1/100

 

Therefore, 15 = P * 1/100 or P = 15*100 = Rs. 1500.

 

Thus, the principal amount is Rs. 1,500.