Aptitude - Compound Interest - Discussion

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.

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.

They asked us to find the diff b/w SI and CI for one year only. But the case is, the interest is credited every 6 month once i.e) half yearly.

Since interest is credited half yearly for an annum,
Compound interest = p[1+(r/2)/100]^2n, where n = 1 year.

S.I calculation is same. Because interest is gonna be constant.

Hope you are clear now.

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.

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.

Just used this formula:

Diffrence = (P * R * R/100 * 100).

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

Earlier - T = 1, R = 10%.
Now T = 2, R = 5%.
(1200 * 5 * 5/100 * 100) = Rs 3.00.

I hope you will understand better!

Thanks.

Time is half yearly. So why in SI = 1200*10*1/(100*2) half yearly is not done.

And in CI 1200 should not be subtracted but to make as SI is calculated yearly, the amount of CI which is calculated half yearly should be doubled to be annually.

Hi friends this might be help you.

In both the cases we should take time 1 year means t = 1 for S.I. and n = 1 for C.I.

But half-yearly data is only given for C.I so, the formula changed for C.I .as per compounded half-yearly.

Yeah. I'm clear. Out off all the above solutions, I could say yours is the best.

S.I calculation will be same if we calculate interest for 1 year & 10% or with summation of two six months with 5% interest. Right?

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.