A sum of ₹10,000 is taken as a loan by Rajesh at a rate of 15% p.a. simple interest for 2 years. But Rajesh could not repay it at the agreed time and asked for an extension of two more years. So, the lender included the interest amount for the period as principal for the next two years at the same rate of interest. The total amount paid by Rajesh at the end of 4 years is:

Correct — A. Simple interest runs for two years, then the lender restarts with a larger principal. Treat it as two separate calculations.

First 2 years on ₹10,000 at 15%:
SI = 10,000 × 15 × 2 ⁄ 100 = ₹3,000
Amount due at year 2 = 10,000 + 3,000 = ₹13,000

That ₹13,000 becomes the principal for the next two years, at the same 15%:
SI = 13,000 × 15 × 2 ⁄ 100 = ₹3,900

Total paid at the end of 4 years = 13,000 + 3,900 = ₹16,900 → option (a)

Why the others are wrong

• (b)
  ₹17,650 — ₹17,650 is more than the scheme can produce. The restart happens once, at year 2, lifting the principal to ₹13,000; two further years at 15% add ₹3,900 and stop there.
• (c)
  ₹15,630 — ₹15,630 is below ₹16,000, which is what plain simple interest for four straight years on ₹10,000 would give. Folding interest into the principal can only raise the total.
• (d)
  ₹18,590 — ₹18,590 is higher even than four years of annual compounding at 15%, which comes to about ₹17,490 — and this loan charges simple interest, not compound.

Simple interest is always charged on the original principal, so four straight years at 15% would cost 60% of ₹10,000 and the borrower would repay ₹16,000.

This question breaks the loan into two blocks. At the end of year 2 the lender treats the amount then due, ₹13,000, as a fresh principal. That is one act of compounding, done by hand, inside an otherwise simple-interest loan.

So the total is neither 10,000 × 1.6 nor 10,000 × 1.15⁴. It is two simple-interest calculations chained, and the restart costs the borrower ₹900.

Key facts

• Simple interest = P × R × T ⁄ 100, computed on the original principal throughout.
• ₹10,000 at 15% for 2 years yields ₹3,000 interest and an amount of ₹13,000.
• ₹13,000 at 15% for 2 years yields ₹3,900 interest, and 13,000 + 3,900 = ₹16,900.
• Four unbroken years of simple interest would have given ₹16,000, so the mid-term restart adds ₹900.

Common traps

• Charging simple interest on ₹10,000 for all four years and answering ₹16,000.
• Compounding annually across the whole four years and reaching roughly ₹17,490.
• Adding the second block's ₹3,900 to ₹10,000 instead of to the new principal of ₹13,000.

No directly related past PYQ was found.