If a moneylender charges 'interest' at the rate of 10 rupees per 100 rupees per half year, payable in advance, then the effective rate of interest per annum is

The moneylender charges 10 rupees per 100 rupees per half year, payable in advance. "Payable in advance" means the interest is paid before receiving the money.

When borrowing for 6 months:

Money requested = 100 rupees

Interest charged in advance = 10 rupees

Money actually received = 100 - 10 = 90 rupees

Amount to be returned after 6 months = 100 rupees

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The actual principal received is 90 rupees, but the interest paid is 10 rupees.

Interest rate for half year = $\dfrac{\text{Interest}}{\text{Principal}} \times 100$

Interest rate for half year = $\dfrac{10}{90} \times 100$

Interest rate for half year = $\dfrac{1}{9} \times 100 = 11.11\%$

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Since the interest is charged every 6 months, for the annual rate, compounding occurs twice per year.

Effective Annual Rate = $(1 + \text{half-yearly rate})^2 - 1$

Effective Annual Rate = $(1 + \dfrac{10}{90})^2 - 1$

$= (1 + \dfrac{1}{9})^2 - 1$

$= (\dfrac{10}{9})^2 - 1$

$= \dfrac{100}{81} - 1$

$= \dfrac{100 - 81}{81}$

$= \dfrac{19}{81}$

$= 0.2345 = 23.45\%$

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Therefore, the effective rate of interest per annum is $23.45\%$.