What principal (₹) will earn ₹1560 as simple interest in 3 years at 4% per…

Concept: simple interest is charged only on the original principal and never on interest that has already been earned, so the same amount is added every year. For a principal P lent at R% per annum for T years, SI = P × R × T / 100. Since P enters that identity linearly, it rearranges directly to P = SI × 100 / (R × T) whenever the interest is the quantity that is known.

Application to this question — the interest earned is given, so the principal is the unknown:

1. Read off the known quantities: SI = ₹1560, R = 4% per annum, T = 3 years, and the principal P is what has to be found.

2. Isolate the unknown in the identity: from SI = P × R × T / 100 we get P = SI × 100 / (R × T).

3. Substitute the given values: P = 1560 × 100 / (4 × 3).

4. Simplify each side of the division: the numerator becomes 156000 and the denominator becomes 12.

5. Divide: P = 156000 / 12 = ₹13000.

Cross-check by a second route: 3 years at 4% per annum is 12% of the principal in total, and 12% of ₹13000 is 0.12 × 13000 = ₹1560, which is exactly the interest stated in the question. Substituting back into the original identity gives 13000 × 4 × 3 / 100 = ₹1560 as well.

Contrast — why the amount formula must not be used here:

The question states that the ₹1560 is earned as simple interest, so the interest-earned reading is the one that applies here and the principal comes out much larger than ₹1560, not smaller than it. The value ₹1392.86 produced by the amount relation is not offered here at all.

Result: the principal is ₹13000.