$1.[5$ pts$.$ each$]$ If the tax rate is $40$ percent, compute the before$-$tax real interest rate and the after$-$tax real interest rate in each of the following cases.

$[$a$]$ The nominal interest rate is $10\%$ and the expected inflation rate is $5\%$;

$[$b$]$ The nominal interest rate is $6\%$ and the expected inflation rate is $2\%$;

$[$c$]$ The nominal interest rate is $4\%$ and the expected inflation rate is $1\%$;