Calculate percentages to $3$ decimal places $($for example, $7\mathrm{.}252\%,$ not just $7\%).$ Assume all bonds pay semiannual coupons. Assume a $365-$day year, unless otherwise indicated.

$1.$ Treasury bills:

a$.$ A Treasury bill has a bid discount yield of $4\mathrm{.}521\%.$ The face value is $$100,000.$ There are $50$ days to maturity.

i$.$ Calculate the current price.

ii$.$ Calculate the bond equivalent yield.

b$.$ A Treasury bill has an ask discount yield of $4\mathrm{.}336\%.$ The face value is $$50,000.$ There are $66$ days to maturity.

i$.$ Calculate the current price.

ii$.$ Calculate the bond equivalent yield.

iii. Calculate the effective annual rate.