Single correct option
On a certain sum, the compound interest (compounded annually) for 2 years is ₹2,100, while the simple interest for the same period at the same rate is ₹2,000. What is the sum?
- A. ₹8,000
- B. ₹10,000
- C. ₹12,000
- D. ₹15,000
Show answer and solution
Answer: (B) ₹10,000
Simple interest for 2 years = 2,000, so SI for one year = ₹1,000 = P × r.
The difference between CI and SI over 2 years (₹100) is the interest earned in year 2 on year 1's interest: 1,000 × r = 100, so r = 10%.
Then P = 1,000 / 0.10 = ₹10,000.
Check: CI = 10,000 × (1.1² − 1) = 2,100 ✓.
Tip: For 2 years, CI − SI = P·r², and SI(1 yr) = P·r; dividing gives r directly.
The difference between CI and SI over 2 years (₹100) is the interest earned in year 2 on year 1's interest: 1,000 × r = 100, so r = 10%.
Then P = 1,000 / 0.10 = ₹10,000.
Check: CI = 10,000 × (1.1² − 1) = 2,100 ✓.
Tip: For 2 years, CI − SI = P·r², and SI(1 yr) = P·r; dividing gives r directly.
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