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Compound Interest for Consecutive Years

CAT 2021 Slot 2 · Quantitative Ability · Medium · CI & SI

This is a medium Quantitative Ability question from the CAT 2021 Slot 2 paper. It tests CI & SI. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are ₹ 806.25 and ₹ 866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to

  1. A.

    931.72

  2. B.

    926.84

  3. C.

    929.48

  4. D.

    934.65

Answer

A

Explanation

In compound interest, the interest accrued in consecutive years grows by the factor (1+r)(1 + r), where rr is the annual rate of interest.

I3=I2(1+r)I_3 = I_2 (1 + r) 866.72=806.25(1+r)  ⟹  1+r=866.72806.25≈1.075003866.72 = 806.25(1 + r) \implies 1 + r = \frac{866.72}{806.25} \approx 1.075003

Interest accrued in the 4th year: I4=I3(1+r)=866.72×1.075003≈931.725I_4 = I_3 (1 + r) = 866.72 \times 1.075003 \approx 931.725 Nearest to 931.72931.72.

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