Pranav borrows a sum of ₹598397 at the rate of 20% per annum simple interest. At the end of the first year, he repays ₹24284 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. Simple interest, so each year's interest is 20% of the principal outstanding during that year.

Year 1 interest = 20% of 598397 = 119679.40
Repayment at the end of year 1 = 24284, taken off the principal
Principal running through year 2 = 598397 − 24284 = 574113

Year 2 interest = 20% of 574113 = 114822.60

At the end of year 2 he clears the principal and both years' interest:
574113 + 119679.40 = 693792.40
693792.40 + 114822.60 = ₹808615 → option (a).

Why the others are wrong

• (b)
  812514 — 812514 overshoots the dues by 3899. The usual way to inflate this line is to charge year 2 on the original 598397 instead of on 574113 — but even that reaches 813471.80, not this figure.
• (c)
  817567 — 817567 sits 8952 above the dues. Nothing here compounds: simple interest never charges interest on unpaid interest, so year 2's 20% applies to 574113 alone.
• (d)
  818513 — 818513 is 9898 above the dues and its digits shadow the correct 808615. Build the answer from its three parts — 574113, 119679.40 and 114822.60 — before choosing.

Simple interest is always charged on the principal outstanding, never on interest that has piled up. A part-payment described as "towards return of principal" lowers that base for every later year.

The first year's interest does not disappear when it goes unpaid. It waits as a due and is settled at the end, but it earns nothing itself. That single distinction is the whole gap between this item and a compound-interest sum.

Key facts

• Simple interest for a year = principal outstanding that year × rate.
• A repayment marked against principal lowers the base for every later year's interest.
• Unpaid simple interest is a flat due carried forward and earns nothing of its own.
• Here the dues are 574113 of principal plus 119679.40 and 114822.60 of interest, totalling 808615.

Common traps

• Charging year 2's interest on the full 598397 and forgetting the repayment
• Compounding the unpaid first-year interest into the second year's base
• Deducting 24284 from the interest bill instead of from the principal

No directly related past PYQ was found.