Question

The difference between simple
interest and compound interest
at the rate of 10% for two years
on an amount is Rs. 2o. find
the principal value ?​

Answer 1

Answer:

• The principal value is Rs 2000.

Step-by-step explanation:

Given that:

• The difference between simple interest and compound interest at the rate of 10% for two years on an amount is Rs. 20.

To Find:

• The principal value.

Let us assume:

• The principal value be x.

Formula used:

In simple interest.

• S.I. = (P × R × T)/100

In compound interest.

• C.I. = P(1 + R/100)ᵀ - P

Where,

• S.I. = Simple interest
• C.I. = Compound interest
• A = Amount
• P = Principal
• R = Rate of interest
• T = Time

Finding the principal value:

According to the question.

⟶ C.I. - S.I. = 20 [∵ C.I. > S.I.]

⟶ P(1 + R/100)ᵀ - P - (P × R × T)/100 = 20

Substituting the values.

⟶ x(1 + 10/100)² - x - (x × 10 × 2)/100 = 20

⟶ x(1 + 0.1)² - x - 20x/100 = 20

⟶ x(1.1)² - x - 0.2x = 20

⟶ x(1.1)² - 1.2x = 20

⟶ x(1.21) - 1.2x = 20

⟶ 1.21x - 1.20x = 20

⟶ 0.01x = 20

⟶ x = 20/0.01

⟶ x = 2000

∴ The principal value = Rs 2000

Answer 2

Given :-

Difference between SI and CI at rate  of 10% for two years

on an amount is Rs. 20.

To Find :-

Principal

Solution :-

SI = PRT/100

C.I. = P(1 + R/100)ᵀ - P

$\sf Let \; principal \; be \; x$

$\sf x\bigg(1 + \dfrac{10}{100}\bigg)^{2} - x - \bigg(\dfrac{x \times 10 \times 2}{100}\bigg) = 20$

$\sf x\bigg(\dfrac{100+10}{100}\bigg)^{2} - x - \bigg(\dfrac{20}{100}\bigg) = 20$

$\sf x\bigg(\dfrac{110}{100}\bigg)^{2} - x - \bigg(\dfrac{x}{5}\bigg) = 20$

$\sf x\bigg(\dfrac{11}{10}\bigg)^{2} - x + \dfrac{x}{5} = 20$

$\sf x\bigg(\dfrac{121}{100}\bigg) -x +\dfrac{x}{5} =20$

$\sf 1.21x - (x + 0.2x) = 20$

$\sf 1.21x - 1.20x = 20$

$\sf x(1.21-1.20) = 20$

$\sf 0.01x = 20$

$\sf x = 2000$