Multiple choice

A principal sum of money is lent out at compound interest compounded annually at the rate of 20% per annum for 2 years . It would give Rs 2410 more if the interest is compounded half year. Find the principal sum.

  1. Rs 120000

  2. Rs 125000

  3. Rs 100000

  4. Rs 110000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For annual compounding, Amount = P(1 + 0.20)^2 = 1.44P. For half-yearly compounding, rate is 10% and time is 4 periods, so Amount = P(1 + 0.10)^4 = 1.4641P. The difference is 0.0241P = 2410, which gives P = 100000.

AI explanation

Let the principal be P. Using the compound interest formula for annual compounding at 20% for 2 years, the amount is P(1.2)^2 = 1.44P. For half-yearly compounding, the rate becomes 10% per half-year over 4 periods, giving an amount of P(1.1)^4 = 1.4641P. The difference is 1.4641P - 1.44P = 0.0241P, which equals Rs 2410, so P = 100000. The principal sum is Rs 100000.

Keep practicing — related questions