Aptitude - Compound Interest - Discussion

S.I = 2 (PRT)/100 ,
T = 0.5,
= 120.

A = P(1+ R/2/100)^2
= 1323.
Then C.I = 1323 - 1200,
= 123
And we get, S.I - C.I = 3.

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.

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.

5/100 is given in the formula. In the formula, there is p*(1+r/100)^n.
Here the rate is given 5% so it has come 5/100.
Hope this helps.

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.

There's a shortcut formula.

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

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

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.