Question

4 7. The difference between compound interest and simple interest on certain sum of money at 10% per annum for 2 years is Rs. 500. Find the sum when the interest is compounded annually​

Answer 1

Answer:

50,000

Step-by-step explanation:

Given:

The difference between Compound interest and Simple interest on a certain sum of money at 10% p.a. for 2 yrs is 500

Principle = p = ?

Rate of interest = r = 10%

Time = n = 2 yrs

Difference = 500 [ CI - SI ]

Solution:

→ $p[(1+i)^n-1] - p * i * t = 500$

→ $p[(1+0.1)^2-1] - p * 0.1 * 2 = 500$

→ $p[(1.1)^2-1] - p * 0.2 = 500$

→ $0.21p - 0.2p = 500$

→ $0.01p = 500$

⇒ p = 50,000

Answer:

50,000

Answer 2

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Given,

• The difference between compound interest and simple interest on certain sum of money at 10% per annum for 2 years is Rs. 500.

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To Find,

• The Sum of the Interest.

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Solution,

Let the Principal of the Interest be 'x'.

As given,

• R = 10%,
• T = 2 years

And,

• C.I. - S.I. = Rs. 500

Finding the Simple Interest in the terms of 'x',

$:\longrightarrow \text{S.I.} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \\ \\:\longrightarrow \text{S.I.} = \frac{x \times 2 \times 10}{100} \\ \\ :\longrightarrow \text{S.I.} = \frac{20}{100} x \\ \\ :\longrightarrow \text{S.I.} = \frac{x}{5} \: \: \: \: \: \: \: \: ... [1]$

Finding Compound Interest in the terms of 'x',

Finding Amount,

$:\longrightarrow \text{A} = \text{P} \bigg( 1 + \frac{\text{R}}{100} \bigg)^{\text{T}} \\ \\ :\longrightarrow \text{A} = x \bigg(1 + \frac{10}{100} \bigg)^{2} \\ \\ :\longrightarrow \text{A} = x \bigg(1 + \frac{1}{10} \bigg)^{2} \\ \\ :\longrightarrow \text{A} = x \bigg( \frac{11}{10} \bigg) ^{2} \\ \\ :\longrightarrow \text{A} = \frac{121x}{100} \: \: \: \: \: \: \: \: ... [2]$

Finding Compound Interest,

$:\longrightarrow \text{C.I.} = \text{A} - \text{P} \\ \\ :\longrightarrow \text{C.I.} = \frac{121x}{100} - x \: \: \: \: \: \: \: ...( \text{By Eq [2]}) \\ \\ :\longrightarrow \text{C.I.} = \frac{121x - 100x}{100} \\ \\ :\longrightarrow \text{C.I.} = \frac{21x}{100} \: \: \: \: \: \: \: \: ... [3]$

According to Question,

$:\longrightarrow \text{C.I.} - \text{S.I.} = \text{Rs.} \: 500$

By Equation [1] and [3],

$:\longrightarrow \frac{21x}{100} - \frac{x}{5} = \text{Rs.} \: 500 \\ \\ :\longrightarrow \frac{21x - 20x}{100} = \text{Rs.} \: 500 \\ \\ :\longrightarrow \frac{x}{100} = \text{Rs.} \: 500 \\ \\ :\longrightarrow {x} = \text{Rs.} \: 500 \times 100 \\ \\ : \longrightarrow {x} = \text{Rs.} \: 50000$

Therefore,

• The value of 'x' is Rs. 50,000.

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Required Answer,

• When, The difference between compound interest and simple interest on certain sum of money at 10% per annum for 2 years is Rs. 500. Then, The Principal would be Rs. 50,000.

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