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

The Correct Option is A

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 \(10.25\%\).