The declared rate of return compounded semi annually equivalent to the effective rate of return 10.25% per annum is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10% p.a.
A declared (nominal) rate r compounded semi-annually gives \(\frac{r}{2}\) per half-year. The effective rate is the actual growth over one year:
\( \displaystyle \left(1 + \frac{r}{2}\right)^2 = 1 + 0.1025 = 1.1025 \)
\( \displaystyle 1 + \frac{r}{2} = \sqrt{1.1025} = 1.05 \)
\( \displaystyle \frac{r}{2} = 0.05,\quad r = 0.10 \)
So the declared rate is 10% p.a. compounded semi-annually.