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

23.45%

The correct answer is Option (4) → 23.45%

Given: Interest charged = ₹10 per ₹100 per half-year, payable in advance.

Nominal half-year rate: $i_{half} = \frac{10}{100} = 0.10$

Since interest is payable in advance, the effective half-year rate:

$i_{half,eff} = \frac{0.10}{1 - 0.10} = \frac{0.10}{0.90} \approx 0.1111$

Effective annual rate (compounded semiannually):

$i_{annual,eff} = (1 + i_{half,eff})^2 - 1 = (1 + 0.1111)^2 - 1 \approx 1.2345 - 1 = 0.2345$

Effective annual rate: 23.45%