What is the nominal rate of interest compounded quarterly if the effective rate of interest on an investment is $5.2 \%$ ?
The nominal rate of interest is $\square \%$ compounded quarterly. (Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as needed.)

Step 1 ：The problem is asking for the nominal rate of interest compounded quarterly if the effective rate of interest on an investment is $5.2 \%$.

Step 2 ：The nominal rate of interest is the rate of interest before the effect of compounding. In this case, the compounding is quarterly. The effective rate of interest is the actual rate of interest after considering the effect of compounding.

Step 3 ：The formula to convert the effective interest rate to the nominal interest rate is: \(\text{Nominal Interest Rate} = n \times [(1 + \text{Effective Interest Rate})^{(1/n)} - 1]\) where n is the number of compounding periods in a year. In this case, n = 4 because the interest is compounded quarterly.

Step 4 ：Substitute the given values into the formula: \(\text{Nominal Interest Rate} = 4 \times [(1 + 0.052)^(1/4) - 1]\)

Step 5 ：Solving the equation gives the nominal interest rate as 5.1016%

Step 6 ：Final Answer: The nominal rate of interest is \(\boxed{5.1016 \%}\) compounded quarterly.