Multiple choice

A sum of money invested at compound interest amounts to Rs $4624$ in $2$ years and to Rs $4913$ in $3$ years. The sum of money is________

  1. Rs $4360$
  2. Rs $4260$
  3. Rs $4335$
  4. Rs $4096$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The ratio of the amount after 3 years to the amount after 2 years is 4913/4624 = 1.0625. Since the amount grows by a factor of (1+r), the principal P satisfies P * (1.0625)^2 = 4624. Solving this gives P = 4624 / (1.0625)^2 = 4096.

AI explanation

The interest earned during the third year is the difference between the amount after three years and the amount after two years, which is 4913 - 4624 = 289. Because 289 represents the interest on the second year amount of 4624, the rate of interest is (289 / 4624) * 100 = 6.25%, or 1/16. Working backwards, the original principal is 4624 / (17/16)^2 = 4624 / 1.1289 = Rs. 4096.

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