Math, asked by staloozakirk, 1 year ago

If the difference of the compound interest and the simple interest on a sum of money for 2 years is 1% of the sum of money then find the annual rate of interest.

Answers

Answered by tejasmba
1

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

 

SI = pnr/100

 

From the problem,

 

N = 2

CI – SI = P*1/100

 

We need to find r.

 

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 = P * 1/100 = P[1+r/100)^2-1-2*r/100]

 

Since P is common on both sides of the equation, they get cancelled.

 

Let us consider the expression within the square brackets.

 

Expanding and subtracting the remaining values, we get

 

1+2r/100+r^2/10000-1-2r/100 = r^2/10000

 

Therefore, 1/100 = r^2/10000.

 

R^2 = 10000/100 = 100

 

Therefore, r = 10%

 

Thus, the rate of interest is 10%.

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