Assume the inflation rate is $2\mathrm{.}06\%$APR$,$ compounded annually. Would you rather earn a nominal return of $4\mathrm{.}53\%$APR$,$ compounded$$ semiannually, or a real return of $2\mathrm{.}67\%$APR$,$ compounded$$ quarterly?$($Note$$: Be careful not to round any intermediate steps less than six decimal$$ places.$)$

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Part $1$

The nominal EAR for $4\mathrm{.}53\%$APR$,$ compounded semiannually is

$$

enter your response here. $($Type your answer in decimal format. Round to six decimal$$ places.$)$