What sum (in ₹) will earn a simple interest of ₹1680 in 2 years at 4% per year…

Concept — Simple interest is interest calculated only on the original principal — it never accumulates on interest already earned. For a principal P invested at R% per annum for T years, SI = (P × R × T) / 100. Rearranging that identity to isolate the principal gives P = (SI × 100) / (R × T).

Application — Here the interest earned is ₹1680, the rate is 4% per annum and the time is 2 years, so the principal is the only unknown.

1. Write the simple-interest identity: SI = (P × R × T) / 100.

2. Substitute the given values: 1680 = (P × 4 × 2) / 100.

3. Combine the rate and the time: 4 × 2 = 8, so 1680 = 8P / 100.

4. Isolate the principal: P = (1680 × 100) / 8.

5. Evaluate: P = 168000 / 8 = 21000, so the sum is ₹21,000.

Cross-check — Carry ₹21,000 forward: 4% of ₹21,000 is ₹840 of interest in one year, and because simple interest does not compound, two years give 2 × ₹840 = ₹1,680 — exactly the interest stated in the question.

Common slips

• Dividing by the rate alone and forgetting the 2-year term gives ₹42,000.

• Doubling the rate to 8% while still applying it for 2 years (dividing by 16 instead of 8) gives ₹10,500.

• Multiplying by (R × T)/100 instead of dividing by it gives ₹134.40.