Pranav borrows a sum of ₹335180 at the rate of 13% per annum simple interest. At the end of the first year, he repays ₹23060 towards return of principal amount borrowed. If Pranav clears all pending dues at the end of the second year, including interest payment that accrued during the first year, how much does he pay (in ₹) at the end of the second year?

Correct — A. Principal ₹3,35,180 at 13% simple interest.

Year 1 interest = 335180 × 13⁄100 = ₹43,573.40
Repayment at the end of year 1 = ₹23,060, all against principal
Principal running through year 2 = 335180 − 23060 = ₹3,12,120

Year 2 interest = 312120 × 13⁄100 = ₹40,575.60

End-of-year-2 payment = remaining principal + both years' interest
= 312120 + 43573.40 + 40575.60
= ₹3,96,269 → option (a).

Why the others are wrong

• (b)
  398876 — ₹3,98,876 overshoots by ₹2,607. The tempting error — charging year 2's interest on the full ₹3,35,180 rather than the reduced ₹3,12,120 — gives ₹3,99,266.80, which is not this figure either, so it is a near-miss decoy.
• (c)
  393949 — ₹3,93,949 is ₹2,320 short. The two interest amounts, ₹43,573.40 and ₹40,575.60, add to a whole ₹84,149, so the total is exact to the rupee and near-misses can be rejected on the last three digits.
• (d)
  388076 — ₹3,88,076 is ₹8,193 short. The clause 'including interest payment that accrued during the first year' is in the stem precisely because year 1's ₹43,573.40 is still outstanding — drop any part of it and you land below the key.

Simple interest is charged on the principal outstanding for that year, and a repayment described as 'towards return of principal' reduces that principal for the year after.

So this is a two-period problem with one moving number: 13% of ₹3,35,180 in year 1, then 13% of ₹3,12,120 in year 2.

Interest never earns interest here. Year 1's ₹43,573.40 simply stays unpaid and is settled at the end, which is what separates this from a compound-interest question.

Key facts

• Simple interest for one year = P × R ⁄ 100, computed on the principal outstanding for that year.
• Here year 1 interest is ₹43,573.40 and year 2 interest is ₹40,575.60, totalling ₹84,149.
• Under simple interest, unpaid interest does not itself attract interest.

Common traps

• Applying year 2's rate to the original ₹3,35,180 after the principal has already been reduced.
• Forgetting that year 1's interest is still owed at the end of year 2.
• Deducting the ₹23,060 repayment a second time from the final payment.

No directly related past PYQ was found.