Aptitude - Simple Interest - Discussion

The rate is always annual(Not necessary to mention).

If it is not mentioned then we have to understand it is 10 p. a.

But in this question interest is calculating at every six months so rate (10/2 =5%).
So, Rate is 5 % for six months,
Now, financier includes interest after 6 months that means He will give interest on the interest that means he will give interest 5% on 5.

So, it is 5*5/100=0.25,
one year interest =5+5+=10%,
But effective interest =10+0.25=10.25,
(here 0.25% is interest on interest)

Doesn't matter if you are taking p=100 or p=200 or p=10.
But interest is always on 100.

If it is given 5% then it means we got an interest of rupees 5 on rupees 100.

If you are taking p=200 and rate is unchanged (5%) then we got 10 rupees interest on 200.
In this case, we are also getting 5 rupees on every 100 rupees.
So in this question, you take principle 100 /200/10 but we get effective interest =10.25.

Thank you @Sushmita.

We can as well take the sum(P) to be 200.

After calculating the simple interest in 6months we get 10,
Add that 10 to the sum making now 210 repeat the tabulation for interest for the remaining months 6.

Then, you get 10.5.

Add the two 10+10.5=20.5.
So. total simple interest is 20.5/200 x 100 which is 10.25.

Why the total sum is 100?

Let the sum be Rs. 100. Then,

S.I. for first half year = Rs. (100 x 10 x 1)/(100x2) = Rs. 5.
S.I. for last half year = Rs. (105 x 10 x 1)/(100x2) = Rs. 5.25.
So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25.
Effective rate = (110.25 - 100) = 10.25%.

Why should we need to consider the amount to be 100?

Why we are charging interest on interest this is simple interest, not compound interest?

If we follow the Compound interest formula it will be easy like watery bubbling.
Suppose principal =100
Amount =p(1+r/100*2)^2n
=100(1+10/2*100)^2*1
=110.25.

Now, CI=A-P
=110.25 -100
=10.25%.

Superb explanation. Thank you all.

6 months is considered 1/2 (Time =1/20).

In the question the person charges for 6 months instead of 1 year.

So effective interest is asked 5% in first 6 and 5.25 in next.