What sum (in ₹) will earn a simple interest of ₹1680 in 2 years at 8% per year…

Concept: Simple interest is charged only on the original principal and never on interest already earned. It is given by SI = P × R × T / 100, where P is the principal, R is the rate per year in percent and T is the time in years. Rearranging the same identity gives the principal directly as P = SI × 100 / (R × T).

Application: Here the interest is ₹1680, the rate is 8% per year and the time is 2 years.

1. Interest earned in one year is 8% of the principal, so the interest over 2 years is 8 × 2 = 16% of the principal.

2. Therefore 16% of the principal equals ₹1680, that is 0.16 × P = 1680.

3. P = 1680 ÷ 0.16 = 1680 × 100 / 16.

4. P = ₹10500.

Cross-check: 8% of ₹10500 is ₹840 of interest in one year, and ₹840 × 2 = ₹1680 over two years, exactly the interest stated in the question.

Common slips:

• Taking the time as 1 year and computing 1680 × 100 / 8 gives ₹21000, because the two-year factor has been dropped.

• Using a two-year factor of 32%, which happens if the rate is doubled or the time is taken as 4 years, gives ₹5250.

• Multiplying instead of dividing, as 1680 × 16 / 100, gives ₹268.8, which is an interest-sized amount and not a principal.