Multiple choice

Over three consecutive years, the additional amount earned by Ritesh from an investment at a fixed annual compound interest rate was Rs. 2,418.75 in the second year and Rs. 2,600.16 in the third year. Based on this pattern, approximately how much interest will Ritesh earn during the fourth year?

  1. Rs. 2,957.17

  2. Rs. 2,759.71

  3. Rs. 2,795.17

  4. Rs. 2,975.71

  5. a
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The interest earned in consecutive years follows a geometric progression because the principal increases by the interest earned. The ratio of the third year interest to the second year interest is 2600.16 / 2418.75 = 1.075. Multiplying the third year interest by this ratio gives 2600.16 * 1.075 = 2795.172.

AI explanation

The additional amount earned in the second year is the interest on the first year's interest, and the additional amount in the third year is the interest on the second year's interest. The compound interest rate is found by dividing the third year's additional interest by the second year's, so the rate is 2600.16 divided by 2418.75, which equals 1.0746 or 7.46%. The total interest in the third year is the second year's total interest plus 2600.16, and we find the second year's total interest by dividing 2418.75 by the interest rate of 0.0746 to get approximately 32435. Adding 2600.16 gives a third year total interest of approximately 35035. The fourth year interest will be 7.46% higher, so we multiply 35035 by 1.0746 to get Rs. 2,795.17.

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