Question

The compound interest on ₹ 4000 for one year
at 5% p.a payable half-yearly is:

Answer 1

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• ➾ Principle = ₹4000
• ➾ Rate = 5 %
• ➾ Time = 1 year
• ➾ Compounded = half yearly

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• ➾ Compound Interest = ?

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❒ Formula Used :

$\large{\blue{\bigstar}}{\underline{\boxed{\red{\sf{C.I = P\bigg(1 + \dfrac{R}{100} \bigg)^T - P}}}}}$

➢Here :

• ➳ C.I = Compound Interest = ?
• ➳ P = Principle = 4000
• ➳ R = Rate = 5 %
• ➳ T = Time = 2T

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Finding the compound interest :

• ➙ C.I = P(1 + R/100)^T - P
• ➙ C.I = 4000(1 + 5/100)^2 - 4000
• ➙ C.I = 4000(1 + 0.05)^2 - 4000
• ➙ C.I = 4000(1.05)^2 - 4000
• ➙ C.I = 4000 × 1.1025 - 4000
• ➙ C.I = 4410 - 4000
• ➙ C.I = Rs.410

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Therefore :

❝ Compound interest on the sum of Rs.4000 is ₹ 410 . ❞

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Answer 2

Solution:

Principal = ₹4000

Time = 1year

Rate = ₹5%

$\tt\bf\underline{\underline{A = P\bigg[1 + \frac{R}{2 \times 100}}\bigg]^{2n}}$

$\tt{=4000\bigg/1 + \frac{5}{2 \times 100}}\bigg/^{2×1}$

$\tt{ = 4000\bigg/1 + \frac{5}{200}\bigg/}^{2}$

$\tt{ = 4000\bigg/\frac{205}{200}\bigg/}^{2}$

$\tt{=4000\bigg/ \frac{41}{40}\bigg/^2}$

$\tt{=4000 \times \frac{1681}{1600}}$

$\tt{=₹4,202.5}$

Amount = ₹4,202.5

Compound Interest = (Amount) - (original principal)

Compound Interest = ₹4,202.5 - 4000

Compound Interest = ₹ 202.5.

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Additional Information

When the interest is compounded annually

$\sf{A =P\bigg/1 + \frac{R}{100}\bigg/^n}$

When the interest is compounded quarterly

$\sf{A = P\bigg/1 + \frac{R}{400}}\bigg/^{4n}$

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Note - Read / as bracket

n = years

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