Question

*What is the difference between compound interests for 2 years and 3 years for Rs. 500 at 10% rate compounded annually?*

1️⃣ ₹ 105
2️⃣ ₹60.50
3️⃣ ₹ 505.50
4️⃣ ₹ 165.50​

Answer 1

Answer :-

• Option 2 is correct.

• The difference between the compound interests is Rs 60.50.

Step-by-step explanation :-

• Before finding the difference, it's essential for us to find the compound interests for 2 years and 3 years for Rs 500 at 10% rate compounded annually.

• To find the compound interest, we will first find the amount using a special formula and then use it to find the compound interest.

• We will find them one by one!

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$\underline{\underline{\sf To \: find \: the \: CI \: for \: 2 \: years :-}}$

We know that :-

$\underline{\boxed{\sf Amount = Principal\Bigg(1 + \dfrac{Rate}{100} \Bigg)^{Time}}}$

Here,

• Principal = Rs 500.
• Rate = 10%.
• Time = 2 years.

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$\longmapsto\underline{\mathfrak{Substituting \: the \: given \: values,}}$

$\longmapsto \boxed{\tt Amount =500\Bigg(1 + \dfrac{10}{100} \Bigg)^{2}}$

$\longmapsto\boxed{\tt Amount = 500\Bigg( \dfrac{1}{1} + \dfrac{10}{100} \Bigg)^{2}}$

$\longmapsto\boxed{\tt Amount = 500\Bigg( \dfrac{1 \times 100 + 10 \times 1}{100} \Bigg)^{2}}$

$\longmapsto\boxed{\tt Amount = 500\Bigg( \dfrac{100 + 10}{100} \Bigg)^{2}}$

$\longmapsto \boxed{\tt Amount = 500 \Bigg(\dfrac{110}{100} \Bigg)^{2}}$

$\longmapsto \boxed{\tt Amount = 500 \times \dfrac{110}{100} \times \dfrac{110}{100}}$

$\longmapsto \boxed{\tt Amount = 500 \times \dfrac{11}{10} \times \dfrac{11}{10}}$

$\longmapsto\boxed{\tt Amount = 500 \times \dfrac{11 \times 11}{10 \times 10}}$

$\longmapsto\boxed{\tt Amount = 500 \times \dfrac{121}{100}}$

$\longmapsto\boxed{\tt Amount = 5 \times \dfrac{121}{1}}$

$\longmapsto\boxed{\tt Amount = 5 \times 121}$

$\longmapsto\overline{\boxed{\tt Amount = Rs \: 605.}}$

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• Now, since we know the amount, therefore let's find the compound interest.

We know that :-

$\underline{\boxed{ \sf CI = Amount - Principal}}$

Here,

• Amount = Rs 605.
• Principal = Rs 500.

Hence,

$\boxed{\tt Compound \: Interest = 605 - 500}$

$\overline{\boxed{\tt Compound \: Interest = Rs \: 105.}}$

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$\underline{\underline{\sf To \: find \: the \: CI \: for \: 3 \: years :-}}$

As we already know,

$\underline{\boxed{\sf Amount = Principal\Bigg(1 + \dfrac{Rate}{100} \Bigg)^{Time}}}$

Here,

• Principal = Rs 500.
• Rate = 10%
• Time = 3 years.

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$\longmapsto\underline{\mathfrak{Substituting \: the \: given \: values,}}$

$\longmapsto\boxed{\tt Amount = 500\Bigg(1 + \dfrac{10}{100} \Bigg)^{3}}$

$\longmapsto\boxed{\tt Amount = 500\Bigg( \dfrac{1}{1} + \dfrac{10}{100} \Bigg)^{3}}$

$\longmapsto\boxed{\tt Amount = 500\Bigg( \dfrac{1 \times100 + 10 \times 1 }{100} \Bigg)^{3}}$

$\longmapsto\boxed{\tt Amount = 500\Bigg( \dfrac{100 + 10}{100} \Bigg)^{3}}$

$\longmapsto\boxed{\tt Amount = 500\Bigg( \dfrac{110}{100}\Bigg) ^{3}}$

$\longmapsto\boxed{\tt Amount = 500 \times \dfrac{110}{100} \times \dfrac{110}{100} \times \dfrac{110}{100}}$

$\longmapsto\boxed{\tt Amount = 500 \times \dfrac{11}{10} \times \dfrac{11}{10} \times \dfrac{11}{10}}$

$\longmapsto\boxed{\tt Amount = 500 \times \dfrac{11 \times 11 \times 11}{10 \times 10 \times 10}}$

$\longmapsto\boxed{\tt Amount = 500 \times \dfrac{1331}{1000}}$

$\longmapsto\boxed{\tt Amount = 5 \times \dfrac{1331}{10}}$

$\longmapsto\boxed{\tt Amount = 1 \times \dfrac{1331}{2}}$

$\longmapsto\boxed{ \tt Amount = 1 \times 665.5}$

$\longmapsto\overline{\boxed{\tt Amount = Rs \: 665.5.}}$

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• Now, since we know the Amount, therefore let's find the compound interest.

As given above :-

$\underline{\boxed{ \sf CI = Amount - Principal}}$

Here,

• Amount = Rs 665.5.
• Principal = Rs 500.

Hence,

$\boxed{\tt Compound \: Interest = 665.5 - 500}$

$\overline{\boxed{\tt Compound \: Interest = Rs \: 165.5.}}$

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• Finally, let's find the difference now since we know the compound interests for 2 and 3 years for Rs 500 at 10% rate compounded annually.

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• Compound interest for 2 years = Rs 105.

• Compound interest for 3 years = Rs 165.5.

Hence, their difference is :-

$\boxed{\implies \bf165.5 - 105}$

$\overline{\boxed{ \implies \bf Rs \: 60.5.}}$

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• We know that in decimals, zeroes after the decimal point has no value. So that means 60.5 and 60.50 have the same value.

• Thus, the difference is Rs 60.50.

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