If the compound interest is compounded half-yearly, then investing a c

1.	If the compound interest is compounded half-yearly, then investing a certain sum at the rate of 10% per annum, the maturity amount after one year is ₹ 13,230. What is the sum? 1. 12,5002. 12,0003. 12,7504. 12,250
Answer» Correct Answer - Option 2 : 12,000 Given: Rate = 10% per annum Maturity Amount after one year = ₹ 13,230 Interest is compounded half yearly Concept Used: For half yearly compound interest just double the time and half the rate then the question is general compound interest question. Formula Used: Amount = Principal[1 + Rate/100]^Time Calculation: Rate = 10%/2 = 5% Time = 1 × 2 = 2 year Amount = Principal[1 + Rate/100]Time ⇒ ₹ 13,230 = Principal[1 + 5/100]² ⇒ ₹ 13,230 = Principal[1 +1/20]² ⇒ ₹ 13,230 = Principal[21/20]² ⇒ ₹ 13,230 = (441/400)Principal ⇒ Principal = ₹ (13230 × 400)/441 ⇒ Principal = ₹ 5292000/441 ⇒ Principal = ₹ 12,000 ∴ The sum is ₹ 12,000

If the compound interest is compounded half-yearly, then investing a certain sum at the rate of 10% per annum, the maturity amount after one year is ₹ 13,230. What is the sum? 1. 12,5002. 12,0003. 12,7504. 12,250

Answer» Correct Answer - Option 2 : 12,000

Given:

Rate = 10% per annum

Maturity Amount after one year = ₹ 13,230

Interest is compounded half yearly

Concept Used:

For half yearly compound interest just double the time and half the rate then the question is general compound interest question.

Formula Used:

Amount = Principal[1 + Rate/100]^Time

Calculation:

Rate = 10%/2 = 5%

Time = 1 × 2 = 2 year

Amount = Principal[1 + Rate/100]Time

⇒ ₹ 13,230 = Principal[1 + 5/100]²

⇒ ₹ 13,230 = Principal[1 +1/20]²

⇒ ₹ 13,230 = Principal[21/20]²

⇒ ₹ 13,230 = (441/400)Principal

⇒ Principal = ₹ (13230 × 400)/441

⇒ Principal = ₹ 5292000/441

⇒ Principal = ₹ 12,000

∴ The sum is ₹ 12,000

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