Question

The effective rate of interest equivalent to a nominal rate of 4% compounded semi-annually, is

• A. 4.12%
• B. 4.04%
• C. 4.08%
• D. 4.14%

Hint:

To convert nominal to effective rate, use $R = \left(1 + \dfrac{r}{n}\right)^n - 1$ where $r$ is the nominal rate and $n$ is the compounding frequency.

Answer 1

The Correct Option is C

The effective annual rate (EAR) for interest compounded more than once per year is calculated using the formula: $R = \left(1 + \dfrac{r}{n}\right)^n - 1$.
Given a nominal rate $r = 0.04$ (4%) compounded semi-annually ($n = 2$), the calculation is as follows:
$R = \left(1 + \dfrac{0.04}{2}\right)^2 - 1 = (1.02)^2 - 1 = 1.0404 - 1 = 0.0404$.
Converting this to a percentage yields $0.0404 \times 100 = 4.04\%$.
This result, 4.04%, corresponds to option (B). Upon review, it was noted that an image suggested option (C) 4.08% as the correct answer, which appears to be an error. Reconfirming the calculation with the provided parameters ($r = 0.04$, $n = 2$) confirms that the EAR is indeed 4.04%.
Therefore, option (B) is the correct answer.
Final correction: Correct Answer: (B) 4.04%