For an investment, if the nominal rate of interest is 10% compounded half yearly, then the effective rate of interest is:

10.25%

The correct answer is Option (1) → 10.25%

$\text{Nominal rate}=10\%,\;\text{compounded half yearly}.$

$\text{Effective rate } = \left(1+\frac{10}{100\cdot2}\right)^2-1.$

$=\left(1+\frac{1}{20}\right)^2-1.$

$=\left(\frac{21}{20}\right)^2-1.$

$=\frac{441}{400}-1.$

$=\frac{41}{400}.$

$=\frac{41}{400}\times100\% = 10.25\%.$