If the difference between the compound interest and simple interest at 17% on a sum of money for 2 years (compounded annually) is…

Question

If the difference between the compound interest and simple interest at 17% on a sum of money for 2 years (compounded annually) is Rs. 433.50, then the sum (in Rs.) is:

1. A. 12,000
2. B. 15,000 (Correct answer)
3. C. 25,000
4. D. 20,000

Correct Answer

Option B — 15,000

Detailed Solution & Explanation

The correct answer is 15,000.

Key Points

• For 2 years, the difference between compound interest and simple interest depends only on the principal and rate through a fixed formula:
• CI − SI (2 years) = P × (R/100)².
• Given the difference = Rs. 433.50 and R = 17%:
• 433.50 = P × (17/100)² = P × 0.0289.
• So P = 433.50 ÷ 0.0289 = Rs. 15,000.
• the 2-year CI−SI gap equals the interest earned in the second year on the first year's interest, which works out to P(R/100)².
• This one formula solves every 'difference between CI and SI for 2 years' question.

Exam Tip

• for 3 years, the difference is P(R/100)²·(3 + R/100) — knowing both the 2-year and 3-year formulas covers virtually all such questions in JKSSB, SSC and banking exams.