Pranav borrows a sum of ₹6,23,305 at the rate of 10% per annum simple interest. At the end of the first year, he repays ₹16,390 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?
- (a)7,25,903
- (b)7,29,937
- (c)7,29,025
- (d)7,38,700
Answer
Why
Correct — B. Simple interest, so each year's interest is 10% of the principal outstanding in that year, and unpaid interest never compounds.
Year 1 interest = 10% of 6,23,305 = ₹62,330.50, unpaid and carried forward
Principal repaid at the end of year 1 = ₹16,390
Principal outstanding for year 2 = 6,23,305 − 16,390 = ₹6,06,915
Year 2 interest = 10% of 6,06,915 = ₹60,691.50
Payment at the end of year 2 = principal still owed + year 2 interest + year 1 interest
= 6,06,915 + 60,691.50 + 62,330.50
= ₹7,29,937 → option (b).
Why the others are wrong
- (a)7,25,903 — ₹7,25,903 falls ₹4,034 short of the ₹7,29,937 due. Dropping the carried-forward first-year interest gives ₹6,67,606.50 instead, so no reading of the stem lands on this figure.
- (c)7,29,025 — ₹7,29,025 sits ₹912 below the correct total — close enough to survive a rough estimate, which is exactly why the three components have to be added to the rupee.
- (d)7,38,700 — ₹7,38,700 needs more interest than 10% allows. Even charging the second year on the full ₹6,23,305 rather than the reduced ₹6,06,915 comes to only ₹7,31,576.
Concept
Under simple interest the principal earns interest and unpaid interest does not — that single rule decides this whole item.
The ₹16,390 is stated to be a repayment of principal, so it cuts the base on which year 2 is charged, from ₹6,23,305 to ₹6,06,915. It does not touch the year 1 interest, which simply stays outstanding.
Clearing all dues at the end of year 2 therefore means three amounts falling on the same day: the principal still owed, the interest for year 2, and the interest for year 1 that was never paid.
Two phrases in the stem are load-bearing and easy to skim past: the ₹16,390 is paid 'towards return of principal amount borrowed', and the final settlement is 'including interest payment that accrued during the first year'.
Key facts
- Simple interest is charged on the principal outstanding, so a part-repayment of principal lowers every later year's interest.
- Unpaid simple interest does not itself earn interest — that is the line between simple and compound.
- 10% of ₹6,23,305 is ₹62,330.50, and 10% of ₹6,06,915 is ₹60,691.50.
- The settlement is ₹6,06,915 + ₹60,691.50 + ₹62,330.50 = ₹7,29,937.
Study next
Common traps
- Treating the ₹16,390 as an interest payment, which would leave year 2's principal at ₹6,23,305.
- Forgetting the first year's interest altogether, which understates the settlement by ₹62,330.50.
- Compounding the interest, which the words 'simple interest' rule out.
SSC dresses simple interest in an untidy principal so the arithmetic cannot be done by pattern — the ₹6,23,305 and the ₹16,390 are there to force the calculation out of you. Percentage-on-percentage work also drives Quant Q.14 of the 13 Sep 2024, 09:00 paper, where 10% and 15% discounts combine.
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