The difference between compound interest and simple interest on a certain sum…

2025

The difference between compound interest and simple interest on a certain sum at the rate of 8% per annum for two years is ₹ 240. What is the sum ?

Answer: B. ₹ 37,500ConceptFor a principal P compounded annually at a rate of r% for two years, the excess of compound interest over simple interest is the interest earned in the…

  1. A.

    ₹ 37,000

  2. B.

    ₹ 37,500

  3. C.

    ₹ 38,000

  4. D.

    ₹ 36,500

Show answer & explanation

Correct answer: B

Concept

For a principal P compounded annually at a rate of r% for two years, the excess of compound interest over simple interest is the interest earned in the second year on the first year’s interest.

Therefore, for two years, CI − SI = P(r/100)2.

Application

  1. Let the principal be P. The annual rate is 8%, and the given difference is ₹240.

  2. Substitute in the two-year identity: 240 = P × (8/100)2.

  3. Simplify: 240 = P × 64/10,000 = 0.0064P.

  4. Divide by 0.0064: P = 240/0.0064 = ₹37,500.

Cross-check

On ₹37,500, simple interest for two years is ₹6,000. Compound interest for two years is ₹37,500 × (1.08)2 − ₹37,500 = ₹6,240, so their difference is ₹240, exactly as given.

Hence, the required sum is ₹37,500.

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