Question

find the difference between C.I and S.I on rs 5000 for 1 year at 2 percentage p.a, if the interest is compounded half yearly​

Answer 1

Given:-

• Principal = 5000
• Time = 1 year
• Rate = 2% p.a.

To Find:-

• Difference between CI and SI after 1 year.

Solution:-

For SI:-

We know,

• $\sf{SI = \dfrac{P \times R\times T}{100}}$

Hence,

$\sf{SI = \dfrac{5000\times 2\times 1}{100}}$

$\sf{SI = 100}$

∴ SI = ₹100

Now

For CI,

We know,

• $\sf{A = P \bigg(1+\dfrac{r}{200}\bigg)^{2n}}$
• CI = A - P

Hence,

$\sf{A = 5000\bigg(1 + \dfrac{2}{100}\bigg)^{2\times1}}$

$\sf{A = 5000\bigg(\dfrac{100+2}{100}\bigg)^2}$

$\sf{A = 5000\bigg(\dfrac{102}{100}\bigg)^2}$

$\sf{A = 5000\bigg(\dfrac{51}{50}\bigg)^2}$

$\sf{A = 5000 \times \dfrac{51}{50} \times \dfrac{51}{50}}$

$\sf{A = 5 \times 51 \times 51}$

A = 13005

Now,

CI = A - P

CI = 13005 - 5000

CI = 8005

∴ CI after 1 year if the interest is compounded half-yearly will be ₹8005

Difference between CI and SI:-

= CI - SI

= 8005 - 100

= 7905

∴ Difference between CI and SI will be of ₹7905 after 1 year.

______________________________________

Answer 2

Given :-

• 5000 for 1 year at 2% p.a, if the interest is  compounded half yearly​.

To Find :-

• The difference between C.I and S.I.

Solution :-

✰  Principle = P = Rs 5000

✰  Rate = R = 2% = 0.02

✰  Compound half yearly = 0.01

---> R = 0.02/2 = 0.01

✰  Time is T= 1 year

✰  Compound half yearly = 2

---> T = 1 × 2 = 2

Simple interest :-

⇒   Principle × Rate × Time

⇒   5000 × 0.01 × 2

⇒  50 × 2

⇒  100

∴ Simple interest = I = Rs 100

Amount :-

$\dashrightarrow\:\: \sf{A = P(1 + R)^T}$

$\dashrightarrow\:\: \sf{A = 5000(1 + 0.01)^2}$

$\dashrightarrow\:\: \sf{A = 5000(1 .01)^2}$

$\dashrightarrow\:\: \sf{A = 5000 \times 1 .0201}$

$\dashrightarrow\:\: \sf{A = 5100.5}$

Compound Interest :-

$\dashrightarrow\:\: \sf{Amount -Principal}$

$\dashrightarrow\:\: \sf{5100.5 -5000}$

$\dashrightarrow\:\: \sf{100.5}$

∴ Compound Interest = 100.5

Difference between C.I and S.I :-

⇒   C.I - S.I

⇒   100.5 - 100

⇒   0.5

∴ The difference between C.I and S.I is 0.5.