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. ₹ 37,500 — ConceptFor 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…
- A.
₹ 37,000
- B.
₹ 37,500
- C.
₹ 38,000
- 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
Let the principal be P. The annual rate is 8%, and the given difference is ₹240.
Substitute in the two-year identity: 240 = P × (8/100)2.
Simplify: 240 = P × 64/10,000 = 0.0064P.
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.