Compound Interest and Simple Interest Difference

CMAT 2021 · Quantitative Techniques & Data Interpretation · Hard · Simple and Compound Interest

The difference between the compound interest and simple interest for two years on a certain sum at a certain rate of interest is Rs. 64. The compound interest for two years is Rs. 704. The principal is

  1. A.

    800

  2. B.

    1600

  3. C.

    2400

  4. D.

    3200

Answer

B

Explanation

Given CI2−SI2=64CI_2 - SI_2 = 64 and CI2=704CI_2 = 704. So SI2=704−64=640SI_2 = 704 - 64 = 640. Simple interest for 1 year = 6402=320\frac{640}{2} = 320. The difference of Rs. 64 is the interest on 1 year's simple interest. So R100×320=64  ⟹  R=20%\frac{R}{100} \times 320 = 64 \implies R = 20\%. Principal P=SI1×100R=320×10020=1600P = \frac{SI_1 \times 100}{R} = \frac{320 \times 100}{20} = 1600.

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