Answer :
Part A. We are asked to determine the effective interest rate given the nominal interest rate. To do that we will use the following formula:
[tex]r=(1+\frac{i}{n})^n-1[/tex]Where:
[tex]\begin{gathered} r=\text{ effective interest rate} \\ i=\text{ nominal interest rate in decimal form} \\ n=\text{ number of compounding periods} \end{gathered}[/tex]Now, since we are given that the interest rate is compounded monthly this means that the value of "n" is:
[tex]n=12[/tex]Now, the interest rate in decimal form is determined by dividing the interest rate by 100, like this:
[tex]r=\frac{5.8}{100}=0.058[/tex]Now, we plug in the values:
[tex]r=(1+\frac{0.058}{12})^{12}-1[/tex]Now, we solve the operations:
[tex]r=0.059567[/tex]In percentage form is 5.9567%
Part B. If the interest rate is compounded continuously we use the following formula:
[tex]r=e^i-1[/tex]Plugging in the values we get:
[tex]r=e^{0.058}-1[/tex]Solving the operations:
[tex]r=0.059715[/tex]In percentage form we get 5.9715%