Single correct option
For a certain principal lent out for 2 years at 12% per annum, the interest earned under annual compounding exceeds the interest earned under simple interest by ₹180. Find the principal.
- A. ₹10,000
- B. ₹11,500
- C. ₹12,500
- D. ₹15,000
Show answer and solution
Answer: (C) ₹12,500
For 2 years, CI − SI = P×(r/100)². This is because the only extra amount CI earns over SI in year 2 is interest-on-interest, i.e., interest on the year-1 interest amount (P×r/100), calculated at rate r again. So 180 = P×(0.12)² = P×0.0144, giving P = 180/0.0144 = ₹12,500. Check: SI for 2 yrs = 12500×0.12×2 = 3000; CI = 12500×(1.12²−1) = 12500×0.2544 = 3180; difference = 180. ✓
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