Mohan borrows a sum of ₹4,22,092 at the rate of 20% per annum simple interest. At the end of the first year, he repays ₹21,679 towards return of principal amount borrowed. If Mohan 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)561347
- (b)564914
- (c)558380
- (d)556367
Answer
Why
Correct — B. Track the principal and the two years of interest separately.
Year 1 interest = 20% of ₹4,22,092 = ₹84,418.40
The ₹21,679 repaid at the end of year 1 is described as a return of principal, so it reduces the principal only:
4,22,092 − 21,679 = ₹4,00,413
Year 2 interest = 20% of ₹4,00,413 = ₹80,082.60
At the end of year 2 he clears the balance principal plus both years of interest, because the first year's interest was never paid:
4,00,413 + 84,418.40 + 80,082.60 = ₹5,64,914 → option (b).
Why the others are wrong
- (a)561347 — ₹3,567 short. With the year-1 interest at ₹84,418.40 and the balance principal at ₹4,00,413, this figure implies a second-year rate of about 19.11%, not the stated 20%.
- (c)558380 — ₹6,534 short of the three amounts due — ₹4,00,413 principal, ₹84,418.40 first-year interest and ₹80,082.60 second-year interest, which add to ₹5,64,914.
- (d)556367 — ₹8,547 short. It fits a second year of 20% charged on about ₹3,57,678 — a principal this problem never produces, since the balance after the ₹21,679 repayment is ₹4,00,413.
Concept
Simple interest is always computed on the principal outstanding, never on accumulated interest.
Two things happen at the end of year 1: interest of ₹84,418.40 falls due but is not paid, and a repayment of ₹21,679 is made against principal. So the interest carries forward untouched while the principal drops to ₹4,00,413.
Year 2 interest is therefore charged on the reduced ₹4,00,413, and the final payment settles three separate amounts: the balance principal and both years of interest.
The wording "towards return of principal amount borrowed" is what fixes this. If the ₹21,679 had been applied to the interest instead, the year-2 interest would still be on ₹4,22,092 and the total would come out different.
Key facts
- Simple interest = P × R × T / 100, charged on the outstanding principal only
- 20% of ₹4,22,092 = ₹84,418.40
- Principal after the year-1 repayment is ₹4,22,092 − ₹21,679 = ₹4,00,413
- 20% of ₹4,00,413 = ₹80,082.60, and ₹4,00,413 + ₹84,418.40 + ₹80,082.60 = ₹5,64,914
Study next
Common traps
- Charging the second year's interest on the original ₹4,22,092
- Forgetting the unpaid first-year interest in the final settlement
- Deducting the ₹21,679 from the final total a second time
SSC uses deliberately awkward principals in these items so that estimating will not separate the options, which sit within a few thousand rupees of each other.
The reliable route is a three-line ledger: interest year 1, revised principal, interest year 2.
Related PYQs
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