# Aptitude - Compound Interest - Discussion

Discussion Forum : Compound Interest - General Questions (Q.No. 13)

13.

The difference between simple interest and compound on Rs. 1200 for one year at 10% per annum reckoned half-yearly is:

Answer: Option

Explanation:

S.I. = Rs | 1200 x 10 x 1 | = Rs. 120. | ||

100 |

C.I. = Rs. | 1200 x | 1 + | 5 | 2 | - 1200 | = Rs. 123. | ||||

100 |

Difference = Rs. (123 - 120) = Rs. 3.

Discussion:

51 comments Page 1 of 6.
Yogeshwar said:
2 years ago

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.

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.

(2)

Dibyajyoti Giri said:
3 years ago

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

(1)

ARCHISA DAS said:
3 years ago

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.

Here the rate is given 5% so it has come 5/100.

Hope this helps.

(1)

Aneesha said:
3 years ago

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.

(2)

Tamalika Roy said:
4 years ago

There's a shortcut formula.

Diff = sum(r/100)^n.

Here,

D = 1200(5/100)^2 (as half-yearly)

= Rs 3.

Diff = sum(r/100)^n.

Here,

D = 1200(5/100)^2 (as half-yearly)

= Rs 3.

(5)

Sovan said:
4 years ago

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.

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.

(2)

BHARAT said:
5 years ago

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

(2)

Arjun said:
5 years ago

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.

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

1200 * 10.25/100 = 123,

CI-SI= 123-120 = 3.

(1)

Naina said:
5 years ago

Because as r=10% for 1 yr so for the half year it would be 5%=5/100.

Ami said:
5 years ago

Why 5/100? Please explain that.

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