A loan taken at 10% per annum by the flat rate method is repaid in 24 equal monthly instalments of Rs. 4,500 each. The amount of the loan is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 90,000
By the flat rate method, interest is charged on the whole loan P for the whole period, and
\( \displaystyle \text{EMI} = \frac{P + I}{n} \)
The total repaid in 24 instalments is
\(4500 \times 24 = 108000\)
The interest for 2 years at 10% is
\( I = P \times 0.10 \times 2 = 0.2P \)
So
\( P + 0.2P = 108000 \)
\( \displaystyle P = \frac{108000}{1.2} = 90000 \)
Why the other options are incorrect
Option (1) Rs. 1,08,000 — Incorrect. This is the total amount repaid, which includes the interest.
Option (2) Rs. 97,200 — Incorrect. This takes 10% off the total repaid; the interest is 20% of the loan, not 10% of the total.
Option (3) Rs. 86,400 — Incorrect. This takes 20% off the total repaid; the interest is 20% of the loan, so the total must be divided by 1.2.