Multiple choice

The rate of interest on two different schemes is the same and it is 20%. But in one of the schemes, the interest is compounded half yearly and in the other, the interest is compounded annually. Equal amounts are invested in the schemes. If the difference of the returns after 2 years is Rs. 482, then what is the principal amount in each scheme?

  1. Rs. 10,000

  2. Rs. 16,000

  3. Rs. 20,000

  4. Rs. 24,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For annual compounding, A = P(1 + 0.20)^2 = 1.44P. For half-yearly, A = P(1 + 0.10)^4 = P(1.1)^4 = 1.4641P. The difference is 0.0241P = 482. P = 482 / 0.0241 = 20000.

AI explanation

Using the compound interest formula, the amount for annual compounding is P(1.2)^2 = 1.44P, and for half-yearly compounding it is P(1.1)^4 = 1.4641P. The difference between these returns is 1.4641P - 1.44P = 0.0241P. Setting this difference equal to Rs 482 gives 0.0241P = 482, so P equals Rs 20,000.

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