Multiple choice

In what time will Rs. $8,000$ amount to Rs. $8,820$ at $10\%$ p.a. interest compounded half-yearly?

  1. $2.5$ year
  2. $4$ year
  3. $3$ year
  4. $1$ year
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Principal = 8000, Amount = 8820, Rate = 10% p.a. compounded half-yearly = 5% per half-year. 8820 = 8000 * (1.05)^n. 8820/8000 = 1.1025. 1.05^2 = 1.1025. So n = 2 half-years = 1 year.

AI explanation

For half-yearly compounding, the annual rate is halved to 5% and the time is doubled to 2n half-years. The compound interest formula gives 8820 equal to 8000 multiplied by (1.05)^(2n). Dividing both sides by 8000 results in 1.1025 equal to (1.05)^(2n), which means 2n equals 2. Therefore, the time is 1 year.

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