Aptitude - Compound Interest - Discussion

There's a shortcut formula.

Diff = sum(r/100)^n.
Here,
D = 1200(5/100)^2 (as half-yearly)
= Rs 3.

Difference between S.I & C.I.

D=P[r/100]^2.

In question given is "reckoned " means "calculating" for half year so take half value in1200 is 600.

Now, 600[10/100]^2=60.

Let, C. I for halfyearly is p[1+(r/200)]^2n.
n=1/2 then 2 * n = 1,
600[1+(10/200)].
600*21/20]=63.
Now, 60-63=60.

I thought the simple interest was also calculated half-yearly. In that case, SI is 122 and CI is 123.

If we calculate the simple interest considering 6 months duration one by one, rate won't be split, P, are remains constant whereas time splits to 1/2. While calculating CI, rate is split whereas time is increased.

Why didn't we take SI to be half-yearly. It should be 60 right?

Very Easy SI and CI both will be calcuated Half Yearly,

New Rate = 10% (divided by) 2 = 5 %.
New Time= 1 year( multiply by)2= 2 Years.

Now SI = (PRT)/100 = (1200 x 5 x 2)/100 =120

Now CI For 1st Year 1200 x 5% = [60].
CI For 2nd Year 1200 x 5%= [60] + 1st Year's 60 x 5% =[3].

Total CI [60 + 60 + 3]= 123.
Total SI =120.
Ans= 123-120 =3.

In the question it is given to compute the difference between CI and SI for 1 year.

Hence : SI= (P*R*T)/100 => (1200*10*1) /100 = 120

Now compute CI for the 1st half year, as it is computed half yearly:

A=P(1+(r/2)/100)^2n , here our n=1/2
=> A=1200(1+(10/2)/100)^2*1/2 => 1200(1+1/20) on computing we get A=1260

So our CI for the first half year is 1260-1200= 60.

Now as we are calculating the CI for 1 year, hence the amount (1260) which we got by calculating the Amount for the first half year becomes our Principal for the second half year.

So again using the formula: P(1+r/100)^n => 1260(1+(10/2)/100)^2*1/2

On computing we get A= 1323, So CI= 1323-1200= 123=> CI at the end of one year.

So as the difference between CI and SI is asked for 1 year.

Hence : CI-SI= 123-120 = 3 Ans.

SI = 120

Given P = 1200, half-yearly compounded so rate becomes half and time becomes double.

1200 * 10.25/100 = 123,
CI-SI= 123-120 = 3.

I think the compound Interest part in the given question is wrong.

Friends,

They told to calculate for 1 year.

Given data is half yearly.

The reason why they calculated for SI without changing the rate of interest is as in the concept of SI the interest rate won't change (constant) so they kept same.

While in CI they changed because it won't be constant. This is the reason guys.