Multiple choice

A sum of Rs. $24000$ is borrowed for $\displaystyle 1\frac{1}{2}$years at the rate of interest $10\%$ per annum compounded semiannually. What is the compound interest ( $x$ )?

  1. $x >$ Rs. $3000$
  2. Rs. $3000 < x <$ Rs. $4000$
  3. Rs. $4000 < x < 5000$
  4. $x >$ Rs. $5000$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Principal = 24000, rate = 10% per annum, compounded semiannually means 5% per half-year. For 1.5 years (3 periods), the amount is 24000 * (1.05)^3 = 24000 * 1.157625 = 27783. The interest is 27783 - 24000 = 3783, which is between 3000 and 4000.

AI explanation

Using the compound interest formula for semiannual compounding, the new rate is 5% for 3 time periods, giving an amount of 24000 multiplied by (1.05)^3. This calculates to 24000 multiplied by 1.157625, resulting in a total amount of Rs. 27783. The compound interest is the total minus the principal of Rs. 24000, yielding Rs. 3783, which safely falls between Rs. 3000 and Rs. 4000.

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