Question

Amount and compound interest earned on Rs. 10000 for 1 year at 9% per annum compounded half yearly is



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Answer 1

Given:

• Principal, P = Rs. 10,000
• Rate, R = 9%
• Time, n (per annum compounded half yearly) = 1 year

To find:

• Amount, A.
• Compound interest, C.I. .

Step-by-step explanation:

We know that it is compounded half yearly and time given is 1 year, so in a year or in one year, there are two half years. So, we will compound the interest two times.

Rate% will also be half.

Rate = 9/2%

♦ A = P(1 + r/100)ⁿ

Where,

A = Amount

P = Principal

r = Rate

n = number of years

Putting the values in the formula, we have:

• A = 10000(1 +9/(2 × 100))²
• A = 10000(1 +9/200)²
• A = 10000((200 +9)/200)²
• A = 10000(209/200)²
• A = 10000 × 209/200 × 209/200
• A = 209/2 × 209/2
• A = 43681/4
• A = Rs. 10920.25

Therefore,

Amount = Rs. 10920.25

♦ C.I. = A - P

Where,

C.I. = Compound interest

A = Amount

P = Principal

Putting the values in the formula, we have:

• C.I. = 10920.25 - 10000
• C.I. = Rs. 920.25

Therefore,

Compound interest = Rs. 920.25

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Answer 2

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Amount and compound interest earned on Rs. 10000 for 1 year at 9% per annum compounded half yearly is?

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Given:

Principal, P = Rs. 10,000

Rate, R = 9%

Time, n (per annum compounded half yearly) = 1 year

To find:

Amount, A.

Compound interest, C.I. .

Step-by-step explanation:

We know that it is compounded half yearly and time given is 1 year, so in a year or in one year, there are two half years. So, we will compound the interest two times.

Rate% will also be half.

Rate = 9/2%

♦ A = P(1 + r/100)ⁿ

Where,

A = Amount

P = Principal

r = Rate

n = number of years

Putting the values in the formula, we have:

A = 10000(1 +9/(2 × 100))²

A = 10000(1 +9/200)²

A = 10000((200 +9)/200)²

A = 10000(209/200)²

A = 10000 × 209/200 × 209/200

A = 209/2 × 209/2

A = 43681/4

A = Rs. 10920.25

Therefore,

Amount = Rs. 10920.25

♦ C.I. = A - P

Where,

C.I. = Compound interest

A = Amount

P = Principal

Putting the values in the formula, we have:

C.I. = 10920.25 - 10000

C.I. = Rs. 920.25

Therefore,

Compound interest = Rs. 920.25

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