Single correct option
A sum of money earns simple interest and annually-compounded interest at 15% per annum for 2 years; the CI exceeds the SI by Rs 180. Find the sum.
- A. Rs 7,200
- B. Rs 7,500
- C. Rs 8,000
- D. Rs 8,500
Show answer and solution
Answer: (C) Rs 8,000
For 2 years, CI − SI = P·r² (a standard identity, since the only extra term in CI is interest-on-interest for one year).
With r = 0.15: r² = 0.0225, so 0.0225P = 180, giving P = 180/0.0225 = 8,000.
Check: SI = 8000 × 0.15 × 2 = 2,400. CI = 8000×(1.15² − 1) = 8000 × 0.3225 = 2,580. Difference = 180. ✓
Tip: for 2 years, CI − SI = P·r² always; no need for the 3-year formula.
With r = 0.15: r² = 0.0225, so 0.0225P = 180, giving P = 180/0.0225 = 8,000.
Check: SI = 8000 × 0.15 × 2 = 2,400. CI = 8000×(1.15² − 1) = 8000 × 0.3225 = 2,580. Difference = 180. ✓
Tip: for 2 years, CI − SI = P·r² always; no need for the 3-year formula.
Saved on this device. Sign in or create a free account to keep it on every device.