Question

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

• A. $10.25\%$
• B. $11.25\%$
• C. $10.125\%$
• D. $11.025\%$

Answer 1

Answer: (A)

$10.25\%$

Answer 2

The formula for the effective rate of interest is:
$\text{Effective Rate} = \left( 1 + \frac{r}{n} \right)^n - 1,$
where $r = 0.1$ (nominal rate) and $n = 2$ (compounding frequency per year).

Substitute into the formula:
$\text{Effective Rate} = \left( 1 + \frac{0.1}{2} \right)^2 - 1 = \left( 1 + 0.05 \right)^2 - 1.$

Simplify:
$\text{Effective Rate} = (1.05)^2 - 1 = 1.1025 - 1 = 0.1025 = 10.25\%.$

Thus, the effective rate of interest is $10.25\%$.