Question

compou o find the compound interest on 210,000 for 12 months at 10% per annum, if the interest is compounded () annually. (i) half yearly, (ii) quarterly ​

Answer 1

Solution

Principal(P) = ₹2,10,000

Time(n) = 12months = 1year

Rate(R) = 10% p.a.

1. Annually

$\bf{A=P\bigg(1+ \dfrac{R}{100}\bigg)^n}$

$\sf{ = 210000 \bigg(1+\dfrac{10}{100} \bigg)^{1}}$

$\sf{ = 210000\bigg(\dfrac{11}{10} \bigg)}$

$\sf{ = 210000 \times\dfrac{11}{10}}$

$\sf{=₹2,31,000}$

CI = Amount - Original Principal

CI = 231000 - 210000

Compound Interest = ₹21000.

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2. Half - yearly

$\bf{A=P\bigg(1+ \dfrac{R}{200}\bigg)^{2n}}$

$\sf{ = 210000 \bigg(1+\dfrac{10}{200}\bigg)^{2 \times 1 = 2} }$

$\sf{ = 210000 \times\dfrac{21}{20} \times\dfrac{21}{20}}$

$\sf{=210000 \times \dfrac{441}{400} }$

$\sf{=₹2,31,525}$

CI = Amount - Original Principal

CI = 231525 - 210000

Compound Interest = ₹21,525.

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3. Quarterly

$\bf{A=P\bigg(1+\dfrac{R}{400}\bigg)^{4n}}$

$\sf{ = 210000 \bigg(1+\dfrac{10}{400}\bigg)^{4 \times 1 = 4} }$

$\sf{ = 210000 \bigg(\dfrac{41}{40} \bigg)^{4} }$

$\sf{ = 210000 \times \frac{41}{40} \times \frac{41}{40} \times \frac{41}{40} \times \frac{41}{40}}$

$\sf{ = 210000 \times \dfrac{2825761}{2560000} }$

$\sf{ =₹2,31,800.707}$

CI = Amount - Original Principal

CI = 231800.707 - 210000

Compound Interest = ₹21,800.707

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Answer 2

Step-by-step explanation:

$solution </p><p>Principal(P) = ₹2,10,000</p><p>Time(n) = 12months = 1year</p><p>Rate(R) = 10% p.a.</p><p></p><p>1. Annually</p><p></p><p>[tex] \bf{A=P\bigg(1+ \dfrac{R}{100}\bigg)^n}$

$\sf{ = 210000 \bigg(1+\dfrac{10}{100} \bigg)^{1}}$

$\sf{ = 210000\bigg(\dfrac{11}{10} \bigg)}$

$\sf{ = 210000 \times\dfrac{11}{10}}$

$\sf{=₹2,31,000}$

CI = Amount - Original Principal

CI = 231000 - 210000

Compound Interest = ₹21000.

$\rule{200pt}{1pt}$

2. Half - yearly

$\bf{A=P\bigg(1+ \dfrac{R}{200}\bigg)^{2n}}$

$\sf{ = 210000 \bigg(1+\dfrac{10}{200}\bigg)^{2 \times 1 = 2} }$

$\sf{ = 210000 \times\dfrac{21}{20} \times\dfrac{21}{20}}$

$\sf{=210000 \times \dfrac{441}{400} }$

$\sf{=₹2,31,525}$

CI = Amount - Original Principal

CI = 231525 - 210000

Compound Interest = ₹21,525.

$\rule{200pt}{1pt}$

3. Quarterly

$\bf{A=P\bigg(1+\dfrac{R}{400}\bigg)^{4n}}$

$\sf{ = 210000 \bigg(1+\dfrac{10}{400}\bigg)^{4 \times 1 = 4} }$

$\sf{ = 210000 \bigg(\dfrac{41}{40} \bigg)^{4} }$

$\sf{ = 210000 \times \frac{41}{40} \times \frac{41}{40} \times \frac{41}{40} \times \frac{41}{40}}$

$\sf{ = 210000 \times \dfrac{2825761}{2560000} }$

$\sf{ =₹2,31,800.707}$

CI = Amount - Original Principal

CI = 231800.707 - 210000

Compound Interest = ₹21,800.707

[ \underline{\rule{200pt}{4pt}}[/tex]