A money lender charges Rs10 for Rs100 per month in advance then effective rate of interest per annum charged by money lender is: [given $\left(\frac{10}{9}\right)^{12} \approx 3.541$]

When the money lender charges Rs 10 for Rs 100 per month in advance:

• The borrower pays Rs 10 immediately (in advance)
• The borrower actually receives only Rs 90
• At month end, the borrower returns Rs 100

The interest of Rs 10 is paid on Rs 90 (the amount actually received), not Rs 100.

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Monthly Interest Rate $= \dfrac{\text{Interest Paid}}{\text{Amount Actually Received}}$

Monthly Rate $= \dfrac{10}{90}$

$= \dfrac{1}{9}$

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Since this happens every month, the monthly rate compounds over 12 months.

The amount grows by a factor of $(1 + \text{monthly rate})^{12}$:

$\left(1 + \dfrac{1}{9}\right)^{12} = \left(\dfrac{9+1}{9}\right)^{12}$

$= \left(\dfrac{10}{9}\right)^{12}$

Given: $\left(\dfrac{10}{9}\right)^{12} \approx 3.541$

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This means Rs 90 becomes Rs 90 × 3.541 = Rs 318.69 after 1 year.

Effective Rate $= \left(\dfrac{10}{9}\right)^{12} - 1$

$= 3.541 - 1$

$= 2.541$

Converting to percentage: $2.541 \times 100 = 254.1\%$

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The effective rate of interest per annum is approximately 254.1% (or 25.41% when considering decimal representation in the options).

The rate is significantly high due to monthly compounding and the fact that interest is paid on Rs 100 while only Rs 90 is actually received.