Multiple choice

If a sum is invested in scheme B at C.I, then amount obtained after 2 year from this scheme is 1.44 times the sum invested. Rate of simple interest for scheme A is half of the rate of compound interest for scheme B. Find out the total interest earned when 8000 was invested in each scheme mentioned above for 2 years.

  1. 5120

  2. 5000

  3. 4800

  4. Can't be determined

  5. None of these
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A Correct answer
Explanation

Scheme B: A = 1.44P, so (1 + r/100)^2 = 1.44, 1 + r/100 = 1.2, r = 20%. Scheme A rate = 10%. Interest A = 8000 * 0.1 * 2 = 1600. Interest B = 8000 * (1.2^2 - 1) = 8000 * 0.44 = 3520. Total = 1600 + 3520 = 5120.

AI explanation

Since the amount after two years is 1.44 times the principal, the compound interest rate for scheme B is the square root of 1.44 minus one, which equals 0.20, or 20%. The simple interest rate for scheme A is half of that, which is 10%. The interest from scheme A on 8000 rupees is 8000 times 10 times 2 divided by 100, equal to 1600 rupees, and the interest from scheme B is 8000 times 1.44 minus 8000, equal to 3520 rupees, making the total interest 5120 rupees.

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