$17.(10$ pts$)$

$($a$)$ Determine the effective rate of interest for $\backslash (4\mathrm{.}275\backslash \%\backslash )$ compounded semiannually. Round your final answer to $3$ decimal places.

$($b$)$ Determine the effective rate of interest for $\backslash (4\mathrm{.}25\backslash \%\backslash )$ compounded continuously. Round your final answer to $3$ decimal places.

$($c$)$ If offered a loan at $\backslash (4\mathrm{.}275\backslash \%\backslash )$ compounded semiannually and a loan at $\backslash (4\mathrm{.}25\backslash \%\backslash )$ compounded continuously, which loan would you take? You must use your responses from parts $($a$)$ and $($b$)$ to explain your reasoning.