Find the effective rate of interest of an investment that earns $2.65 \%$ compounded semiannually. \% Round to three decimal places

Step 1 ：We are given that the nominal interest rate (i) is 2.65%, the number of compounding periods per year (n) is 2 (since it's compounded semiannually), and the time (t) is 1 year.

Step 2 ：We convert the nominal interest rate from percentage to decimal form: \(i = 0.0265\)

Step 3 ：We substitute the values into the formula for the effective rate of interest: \((1 + i/n)^{nt} - 1\)

Step 4 ：Substituting the values we get: \((1 + 0.0265/2)^{2*1} - 1\)

Step 5 ：Solving the above expression, we get the effective rate of interest as 0.026675562499999916

Step 6 ：However, the question asks for the answer to be rounded to three decimal places. So, we round off the above value to get 0.027

Step 7 ：Final Answer: The effective rate of interest of an investment that earns 2.65% compounded semiannually is \(\boxed{2.7 \%}\)