For an investment, if the nominal rate of interest is 10% compounded half yearly, then the effective rate of interest is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10.25%
$\text{Nominal rate}=10\%,\;\text{compounded half yearly}.$
$\text{Effective rate } = \left(1+\frac{10}{100\cdot2}\right)^2-1.$
$=\left(1+\frac{1}{20}\right)^2-1.$
$=\left(\frac{21}{20}\right)^2-1.$
$=\frac{441}{400}-1.$
$=\frac{41}{400}.$
$=\frac{41}{400}\times100\% = 10.25\%.$