Simple vs Compound Interest Sum Calculation

CMAT 2023 · Quantitative Techniques & Data Interpretation · Medium · Simple Interest

A certain sum of money earns a simple interest of ₹ 800 over 2-year period. The same sum of money invested at the same rate of interest and same period on a compound interest basis earns an interest of ₹ 900. What is the sum?

  1. A.

    ₹1,200

  2. B.

    ₹1,600

  3. C.

    ₹2,000

  4. D.

    ₹2,400

Answer

B

Explanation

Simple interest per year = 8002=400\frac{800}{2} = 400. Difference between CI and SI for 2 years = 900−800=100900 - 800 = 100. This ₹100 is the interest on ₹400 for 1 year. Rate r=100400×100=25%r = \frac{100}{400} \times 100 = 25\%. Since SI=P×r×t100⇒800=P×25×2100⇒P=1600SI = \frac{P \times r \times t}{100} \Rightarrow 800 = \frac{P \times 25 \times 2}{100} \Rightarrow P = 1600.

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