Multiple choice

A sum of money becomes Rs. 4,800 after 2 years and Rs. 6,000 after 4 years on compound interest. Find the principal sum.

  1. Rs. 3,840

  2. Rs. 3,600

  3. Rs. 4,000

  4. Rs. 4,250

  5. Rs. 4,500
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A Correct answer
Explanation

For compound interest, the principal P after n years becomes A = P(1+r)^n. Given A(2) = 4800 and A(4) = 6000, the ratio A(4)/A(2) = (1+r)^2 = 6000/4800 = 1.25. Thus, P = A(2) / (1+r)^2 = 4800 / 1.25 = 3840.

AI explanation

Since the sum amounts to 4800 in 2 years and 6000 in 4 years, the interest for the 2-year period between year 2 and year 4 is 1200. Using the compound interest ratio, the principal multiplied by the rate factor squared equals 4800, and this same principal multiplied by the rate factor to the fourth power equals 6000. We can divide 6000 by 4800 to find the rate factor squared is 1.25, meaning the principal amount for the first two years was 4800 divided by 1.25, which equals 3840. To find the initial principal, divide 3840 by 1.25 again to get Rs. 3840.

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