Multiple choice

On a certain sum at a certain rate of interest, interest being compounded per annum the compound interest for the second year and the fourth year are ₹4800 and ₹6912 respectively. Which of the following gives the value of the sum (in ₹)?

  1. 16000

  2. 32000

  3. 24000

  4. 20000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For compound interest, the ratio of interest in consecutive years is (1 + r). Here, (1 + r)^2 = 6912 / 4800 = 1.44, so 1 + r = 1.2. The interest in the second year is P * r * (1 + r) = 4800. P * 0.2 * 1.2 = 4800, so P * 0.24 = 4800, P = 20000.

AI explanation

In compound interest, the ratio of the interests for successive years is equal to the common ratio, so the growth factor from the second year to the fourth year is (6912 / 4800)^(1/2) = (1.44)^(1/2) = 1.2, meaning the rate of interest is 20%. The interest for the first year would be 4800 / 1.2 = 4000, which equals 20% of the principal. Therefore, the principal sum is 4000 * 5 = 20000.

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