$3.$ Compounding Frequency $(6$ points$)$

You are holding a security which will pay you $100$ dollars for sure in $2$ years. The risk$-$free rate is

$5\%$ in semiannual APR.

$($a$)(2$ points$)$ What is the value of this security today under semiannual compounding? $[$keep $6$

decimal places$]$

$($b$)(2$ points$)$ What is the rate per annum in continuous compounding that is equivalent to $5\%$

semiannual APR? $[$keep $6$ decimal places$]$

$($c$)(2$ points$)$ What is the value of this security today under continuous compounding? Is your

result the same as in $($a$)?[$keep $6$ decimal places$]$