A loan of Rs. 2,00,000 at 6% per annum compounded monthly is repaid in 24 equal monthly instalments at the end of each month by the reducing balance method. The total interest paid is (Given \((1.005)^{24} = 1.1272\))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 12,679.36
By the reducing balance method, with P = 200000, i = 0.06 ÷ 12 = 0.005 and n = 24,
\( \displaystyle \mathrm{EMI} = \frac{P\,i\,(1+i)^n}{(1+i)^n - 1} \)
\( \displaystyle = \frac{1000 \times 1.1272}{0.1272} \)
\(\approx 8861.64\)
The total interest paid is everything paid minus the loan:
\(nR - P = 24 \times 8861.64 - 200000\)
\(= 212679.36 - 200000 = 12679.36\)
Why the other options are incorrect
Option (1) Rs. 24,000 — Incorrect. This is 6% of Rs. 2,00,000 for 2 years, the flat rate interest on the original loan.
Option (3) Rs. 2,12,679.36 — Incorrect. This is the total amount paid in 24 instalments, which includes the loan itself.
Option (4) Rs. 8,861.64 — Incorrect. This is one EMI, not the total interest.