A vendor lends 74,000 rupees at a rate of 12% compound interest per annum, compounded annually. Find the interest for the 3rd year.

Correct — C.
Each year's interest is 12% of the amount at the start of that year.

Year 1: 74,000 × 12⁄100 = 8,880, so the amount becomes 82,880
Year 2: 82,880 × 12⁄100 = 9,945.60, so the amount becomes 92,825.60
Year 3: 92,825.60 × 12⁄100 = 11,139.072

Round to two decimals: 11,139.07 → option (c)

Why the others are wrong

• (a)
  10,000.90 — 10,000.90 matches none of the yearly interests: 8,880 in year 1, 9,945.60 in year 2, 11,139.07 in year 3. Each is 1.12 times the one before.
• (b)
  11,000.50 — 11,000.50 would need an amount of about 91,671 at the start of year 3, but 74,000 × 1.12² = 92,825.60, whose 12% is 11,139.07.
• (d)
  12,000 — 12,000 is 12% of 1,00,000, but the amount after two years is only 92,825.60. The year-3 interest cannot reach 12,000.

Under compound interest, each year's interest is charged on the principal plus all interest already added. So the yearly interest itself grows by the factor (1 + r⁄100).

Interest for year n = P × (1 + r⁄100)ⁿ⁻¹ × r⁄100

For n = 3 and r = 12: 74,000 × 1.12² × 0.12 = 74,000 × 0.150528 = 11,139.072.

Key facts

• Interest for the nth year under annual CI = P × (1 + r⁄100)ⁿ⁻¹ × r⁄100
• 1.12² = 1.2544 and 1.12³ = 1.404928
• First-year CI interest equals first-year simple interest, here 8,880

Common traps

• Using the amount after three years (× 1.12³) instead of after two (× 1.12²) as the base for year 3
• Taking 12% of the original 74,000, which is the simple-interest figure 8,880 for every year

No directly related past PYQ was found.