The following tables is an example of market quotes for Treasury Bills and Notes. For the questions below assume that the Treasury Notes pay only one coupon every year.

Maturity Coupon $1$mo $$

$3$mo $$

$6$mo $$

$1$yr $0\mathrm{.}7502$yr $0\mathrm{.}3753$yr $1\mathrm{.}5004$yr $0\mathrm{.}7505$yr $2\mathrm{.}375$

Yield $0\mathrm{.}0250\mathrm{.}0350\mathrm{.}0710\mathrm{.}1620\mathrm{.}3280\mathrm{.}5820\mathrm{.}8881\mathrm{.}129$

$($a$)$ What are the zero$-$rates for the maturities shown in the table above? Assume all the rates in this exercise are discretely compounded rates.

$($b$)$ What is the implied forward rate for an investment starting in $1$ year and lasting for $2$ years?

$($c$)$ You are about to enter a Forward Rate Agreement starting in $1$ year and lasting for $2$ years, for a rate of $0\mathrm{.}5\%$ and a notional of $$100,000.$ What are the cash flows of this agreement?

$($d$)$ What is the present value of the FRA above?