Question

find the amount and the compound interest, p-2000,R-5,T-2.​

Answer 1

Solution:-

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◍ Here, the question has given us the principal, rate of interest and time that is Rs. 20,000, 5% per annum and for 2 years respectively. Now, the question has asked us to find the compound interest on it. So to get the answer we need to apply the formula of amount first then we will subtract the principal from amount to get CI.

ANSWER:-

◈ The amount is Rs. 2,205.

◈ The CI is Rs. 205.

GIVEN:-

☆ Principal = Rs. 2000

☆ Rate of Interest = 5% per annum

☆ Time = 2 years

TO FIND:-

↠ Compound Interest = ?

FORMULA:-

⬤ Amount = P[1 + (R / 100)]^t

⬤ CI = Amount - Principal

SOLVING BY APPLYING THE FORMULA:-

⇨ Principal = Rs. 20,000

⇨ Rate = 5%

⇨ Time = 2 years

⇨ Amount = P[1 + (R / 100)]^n

➢ Amount = 2000[1 + (5 / 100)]²

➢ Amount = 2000[100 + 5 / 100]²

➢ Amount = 2000[105 / 100]²

➢ Amount = 2000 × 11,025 / 10,000

➢ Cancelling the zeros.

➢ Amount = 2 × 11,025 / 10

➢ Amount = 22,050 / 10

➢ Amount = 22,050 / 10 = 2,205

➢ Amount = Rs. 2,205

Thus, the amount is Rs. 2,205.

⇨ Compound Interest = Amount - Principal

➢ CI = 2,205 - 2000

➢ CI = 2,205 - 2000 = 205

➢ CI = Rs. 205

Hence, we got the answer. The CI is Rs. 205.

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Answer 2

Answer :-

• The amount is Rs 2205.
• The compound interest is Rs 205.

To find :-

• The amount and the compound interest.

Step-by-step explanation :-

• Here, the principal, rate and time have been given to us. We have to find the amount and compound interest.

• Before finding the compound interest, let's find the amount!

We know that :-

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

Here,

• Principal = Rs 2000.
• Rate = 5% per annum.
• Time = 2 years.

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Hence,

$\rm Amount =2000 \bigg(1 + \dfrac{5}{100} \bigg)^{2}$

Reducing 5/100 to it's simplest form,

$\rm Amount =2000 \bigg(1 + \dfrac{1}{20} \bigg)^{2}$

The LCM of 1 and 20 is 20, so adding the fractions using their denominators,

$\rm Amount =2000 \bigg( \dfrac{1 \times 20 + 1 \times 1}{20} \bigg)^{2}$

On simplifying,

$\rm Amount =2000 \bigg( \dfrac{20 + 1}{20} \bigg)^{2}$

Adding 1 to 20,

$\rm Amount =2000 \bigg( \dfrac{21}{20} \bigg)^{2}$

The power here is 2, so removing the brackets and multiplying 21/20 with itself 2 times,

$\rm Amount =2000 \times \dfrac{21}{20} \times \dfrac{21}{20}$

Let's multiply 21/20 with itself first,

$\rm Amount =2000 \times \dfrac{21 \times 21}{20 \times 20}$

On multiplying,

$\rm Amount =2000 \times \dfrac{441}{400}$

Cutting off the zeroes,

$\rm Amount =20 \times \dfrac{441}{4}$

Reducing the numbers,

$\rm Amount =5 \times \dfrac{441}{1}$

Now let's multiply the remaining numbers since we can't reduce them anymore.

$\rm Amount =5 \times 441$

Multiplying 5 with 441,

$\overline{ \boxed{ \rm Amount =Rs \: 2205}}$

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• Now, as we know the amount, let's find the compound interest!

We know that :-

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

Here,

• Amount = Rs 2205.
• Principal = Rs 2000.

Hence,

$\boxed{ \bf CI =2205 - 2000}$

$\overline{ \boxed{\bf CI =Rs \: 205}}$

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Abbreviations used :-

CI = Compound Interest.