Question

The difference between the simple interest and the compound intrest
on Rs. 1250 for 2yr at 8% per annun will be​

Answer 1

Given:

• Principal - Rs. 1250
• Rate - 8 %
• Time = 2 years

What To Find:

We have to find the -

• Difference between the simple interest and the compound interest.

How To Find:

To find we have to -

• First, we have to find the simple interest using a definite formula.
• Next, we have to find the compound interest using definite formulas.
• Then, find the difference between the simple interest and the compound interest.

Formulas Needed:

The formulas are -

$\bf 1. \: SI = \dfrac{PRT}{100} \\\\ \bf 2. \: i. \: A = P + \bigg( 1 + \dfrac{R}{100} \bigg)^T \\\\ \bf 2. \: ii. \: CI = A - P$

Abbreviations Used:

• P = Principal
• R = Rate
• T = Time
• A = Amount
• SI = Simple Interest
• CI = Compound Interest

Solution:

• Finding the SI.

Using the formula,

$\sf \longmapsto SI = \dfrac{PRT}{100}$

Substitute the values,

$\sf \longmapsto SI = \dfrac{1250 \times 8 \times 2}{100}$

Solve the numerator,

$\sf \longmapsto SI = \dfrac{20000}{100}$

Divide 20000 by 100,

$\sf \longmapsto SI = Rs. \: 200$

∴ Thus, the SI is Rs. 200.

⸻⸻⸻⸻

• Finding the CI.

Finding amount first.

Using the formula,

$\sf \longmapsto A = P \bigg( 1 + \dfrac{R}{100} \bigg)^T$

Substitute the values,

$\sf \longmapsto A = 1250 \bigg( 1 + \dfrac{8}{100} \bigg)^2$

Solve the brackets,

$\sf \longmapsto A = 1250 \bigg( \dfrac{108}{100} \bigg)^2$

Remove the brackets,

$\sf \longmapsto A = 1250 \times \dfrac{108}{100} \times \dfrac{108}{100}$

Solve the fractions,

$\sf \longmapsto A = 1250 \times \dfrac{11664}{10000}$

Divide 11664 by 10000,

$\sf \longmapsto A = 1250 \times 1.1664$

Multiply 1250 by 1.1664,

$\sf \longmapsto A = Rs. \: 1458$

Finding the CI next.

Using the formula,

$\sf \longmapsto CI = A - P$

Substitute the values,

$\sf \longmapsto CI = 1458 - 1250$

Subtract the amount,

$\sf \longmapsto CI = Rs. \: 208$

∴ Thus, the CI is Rs. 208.

⸻⸻⸻⸻

• Finding the difference.

Here,

• SI = Rs 200
• CI = Rs. 208

So, we will be,

$\sf \longmapsto 208 - 200$

Subtract the amount,

$\sf \longmapsto Rs. \: 8$

∴ Thus, the difference is Rs. 8.

⸻⸻⸻⸻

Final Answer:

∴ Thus, the difference between the simple interest and the compound interest is Rs. 8.

Answer 2

Given :

• Principal (P) = Rs. 1250
• Time (T) = 2 years
• Rate (R)= 8%

To Find :

• Difference between simple interest And compound interest

Solution :

Finding simple Interest

⟹ SI = P × R × T/100

⟹ SI = 1250 × 2 × 8/100

⟹ SI = 20000/100

⟹ SI = 200

Now, Compound interest

⟹ CI = P (1 + R/100)ⁿ - P

⟹ CI = 1250 (1 +8/100)² - 1250

⟹ CI = 1250 × 108/100 × 108/100 - 1250

⟹ CI = 1458000/10

⟹ CI = 1458 - 1250

⟹ CI = Rs. 208

Difference between CI and SI

⟹ 208 - 200

⟹ Rs. 8

∴ Difference between simple interest And compound interest is Rs. 8