Question

b) If the difference between the compound interest and simple interest on a sum of money for 2 years is 1% of
the sum of money, then find the annual rate of interest.
[3]​

Answer 1

Answer:

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%.