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Simple and Compound Interest Calculation

CAT 2025 Slot 1 · Quantitative Ability · Medium · Simple Interest

This is a medium Quantitative Ability question from the CAT 2025 Slot 1 paper. It tests Simple Interest. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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At a certain simple rate of interest, a given sum amounts to Rs. 13920 in 3 years, and to Rs. 18960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as before but with interest compounded every 6 months, then the total interest earned, in rupees, would have been nearest to

  1. A.

    3221

  2. B.

    3180

  3. C.

    3150

  4. D.

    3096

Answer

A

Explanation

Difference in time = 6.5−3=3.56.5 - 3 = 3.5 years. Difference in amount = 18960−13920=504018960 - 13920 = 5040. Interest per year under simple interest = 5040/3.5=14405040 / 3.5 = 1440. Interest in 3 years = 3×1440=43203 \times 1440 = 4320. Principal P=13920−4320=9600P = 13920 - 4320 = 9600. Rate of interest R=(1440/9600)×100=15%R = (1440 / 9600) \times 100 = 15\% per annum. For compounding half-yearly over 2 years (n=4n = 4 periods): half-yearly rate r=7.5%=0.075r = 7.5\% = 0.075. Amount A=9600×(1.075)4=9600×1.335469=12820.5A = 9600 \times (1.075)^4 = 9600 \times 1.335469 = 12820.5. Compound Interest = 12820.5−9600=3220.5≈322112820.5 - 9600 = 3220.5 \approx 3221.

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