What is the compound interest on Rs. 8000 for 2 year at 10% per annum?

Correct — B. Compound interest adds each year's interest to the principal before the next year's interest is worked out.

Year 1 interest = 10% of 8000 = 800
Amount after year 1 = 8000 + 800 = 8800
Year 2 interest = 10% of 8800 = 880

CI = 800 + 880 = 1680 → option (b)
Check: 8000 × 1.1² = 8000 × 1.21 = 9680, and 9680 − 8000 = 1680

Why the others are wrong

• (a)
  1600 — 1600 is the simple interest: 8000 × 10% × 2. It misses the 80 earned in year 2 on year 1's interest of 800.
• (c)
  1650 — For 2 years, CI − SI = P × (r⁄100)² = 8000 × 0.01 = 80, so CI = 1600 + 80 = 1680. 1650 is 30 short of that.
• (d)
  1700 — 1700 is 100 above the simple interest, but at 10% for 2 years the gap is only 8000 × 0.1² = 80. That puts CI at 1680, 20 below this option.

Compound interest earns interest on interest already earned. With yearly compounding, Amount = P × (1 + r⁄100)ⁿ and CI = Amount − P.

At 10% for 2 years the multiplier is 1.1 × 1.1 = 1.21, so CI is 21% of the principal: 21% of 8000 = 1680.

The extra over simple interest is year 2's interest on year 1's interest: 10% of 800 = 80.

Key facts

• Amount = P(1 + r⁄100)ⁿ when interest is compounded yearly.
• At 10% a year for 2 years, CI = 21% of P and SI = 20% of P.
• For 2 years, CI − SI = P(r⁄100)²: here 8000 × (10⁄100)² = 80.

Common traps

• Answering the simple interest, 1600, and dropping year 2's interest on interest.
• Reporting the amount (9680) when the question asks for the interest (1680).

No directly related past PYQ was found.