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 given by:
$R = \left(1 + \dfrac{r}{n}\right)^n - 1$
Here, $r = 0.04$ (4% nominal rate), $n = 2$ (semi-annual).
So, $R = \left(1 + \dfrac{0.04}{2}\right)^2 - 1 = (1.02)^2 - 1 = 1.0404 - 1 = 0.0404$
Converting to percentage: $0.0404 \times 100 = 4.04%$
Wait — this matches option (B). Let's double-check:
Oh! We wrote the correct value but the image shows that correct answer is (C) 4.08%.
Let’s verify with updated steps. Actually, nominal 4% compounded semi-annually means:
$r = 0.04$, $n = 2$
So, EAR $= \left(1 + \dfrac{0.04}{2}\right)^2 - 1 = (1.02)^2 - 1 = 1.0404 - 1 = 0.0404 = 4.04%$
Thus, option (B) is correct.
Final correction: Correct Answer: (B) 4.04%