A money lender charges Rs10 for Rs100 per month in advance then effective rate of interest per annum charged by money lender is: [given \(\left(\displaystyle\frac{10}{9}\right)^{12} = 3.541\)]
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 254.1%
Interest is charged in advance: the borrower receives Rs. 90 now and repays Rs. 100 after a month. So Rs. 10 is the interest on Rs. 90 for one month:
\( \displaystyle i = \frac{10}{90} = \frac{1}{9} \) per month
The effective annual rate with monthly compounding is
\( \displaystyle r_{\text{eff}} = (1 + i)^{12} - 1 = \left(\frac{10}{9}\right)^{12} - 1 \)
\(= 3.541 - 1 = 2.541 = 254.1\%\)
Why the other options are incorrect
Option (1) 23.45% — Incorrect. It does not equal \(\left(\frac{10}{9}\right)^{12} - 1\).
Option (3) 24.41% — Incorrect. It does not equal \(\left(\frac{10}{9}\right)^{12} - 1\) either.
Option (4) 10% — Incorrect. This is the charge per month on Rs. 100. It ignores both the advance payment and the compounding over 12 months.
Note: It seems that there is a mistake in the original NTA question, which prints Option (2) as 25.41%, with the decimal point misplaced. The effective rate is 254.1%, and no printed option gave it. For the benefit of students and to ensure that the question is correct and has a single valid answer, Option (2), the answer given by NTA, has been changed to 254.1%.