A person has taken a loan of Rs. 40,000 for 3 months from a lender who has deducted Rs. 2,000 as interest at the time of lending. Then the effective rate of interest charged per annum by lender is (given \((1.0526)^4 = 1.2275\)):
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 22.75%
The interest is deducted in advance: the borrower actually receives Rs. 38,000 and repays Rs. 40,000 after 3 months. So Rs. 2,000 is the interest on Rs. 38,000 for one quarter:
\( \displaystyle i = \frac{2000}{38000} = 0.0526 \) per quarter
A year has 4 quarters, so the effective annual rate is
\(r_{\text{eff}} = (1 + i)^4 - 1\)
\(= (1.0526)^4 - 1\)
\(= 1.2275 - 1 = 0.2275\)
So the effective rate is 22.75% per annum.
Why the other options are incorrect
Option (1) 10.50% — Incorrect. It does not equal \((1.0526)^4 - 1\).
Option (2) 21% — Incorrect. This is about \(4 \times 5.26\%\), the nominal rate. It ignores the compounding of the quarterly interest.
Option (4) 16.75% — Incorrect. It does not equal \((1.0526)^4 - 1\) either.