Question

Find the difference between the compound interest and the simple intersest on₹4000 for 2 years at 10%


please anyone help me to explain this question ​

Answer 1

$\underline{ \sf \large{Solution- }}$

Here it is given that,

• Principal = Rs. 4000
• Time = 2 years
• Rate of interest = 10%

➢ We have to find the difference between the compound interest and the simple interest.

Now,

$\tt\implies \boxed{ \sf S.I = \tt \dfrac{P \times R \times T}{100} }$

$\tt\implies \sf \tt \dfrac{4000 \times 10\times 2}{100}$

$\tt\implies \sf S.I = Rs. \: 800$

Now,

$\tt\implies \boxed{ \sf Amount = \tt P \left[ 1 + \dfrac{ R }{100} \right]^{n } }$

$\tt\implies \sf \tt 4000 \left[ 1 + \dfrac{ 10 }{100} \right]^{2 }$

$\tt\implies \sf \tt 4000 \left[ 1 + \dfrac{ 1 }{10} \right]^{2 }$

$\tt\implies \sf \tt 4000 \left[ \dfrac{ 11 }{10} \right]^{2 }$

$\tt\implies \sf \tt 4000 \times \dfrac{ 121 }{100}$

$\tt\implies \sf Amount = \sf Rs. \tt\: 4840$

Now,

• C.I = Amount - Principal

⟹ C.I = 4840 - 4000

⟹ Compound interest = Rs. 840

Now,

➢ Difference between C.I and S.I :

⟹ 840 - 800

⟹ Rs. 40

• Therefore, the answer is Rs. 40

Answer 2

Given :-

• Principle = Rs. 4000
• Time = 2 years
• Rate = 10%

To Find :-

Find the difference between the compound interest and the simple interest

Solution :-

We know that

SI = PRT/100

CI = P(1 + R/100)ⁿ - P

For SI

SI = 4000 × 10 × 2/100

SI = 40 × 10 × 2

SI = 400 × 2

SI = Rs. 800

For CI

CI = P(1 + R/100)ⁿ - P

CI = 4000(1 + 10/100)² - 4000

CI = 4000(100 + 10/100)² - 4000

CI = 4000(110/100)² - 4000

CI = 4000(11/10)² - 4000

CI = 4000 × 121/100 - 4000

CI = 40 × 121 - 4000

CI = 4840 - 4000

CI = Rs. 840

Now

Difference = CI - SI

Difference = 840 - 800

Difference = Rs. 40