Four Treasury securities data from today's Wall Street Journal are provided below:

Bond

Treasury

Security

Maturity

Annual

Coupon

Price

Par

Value

A

T$-$bill

$6$ months

$0\%$

$$984\mathrm{.}0240$

$$1,000$

B

T$-$bill

$1$ year

$0\%$

$$966\mathrm{.}1280$

$$1,000$

C

T$-$note

$18$ months

$3\mathrm{.}875\%$

$$999\mathrm{.}0625$

$$1,000$

D

T$-$note

$2$ years

$4\mathrm{.}625\%$

$$1,009\mathrm{.}0625$

$$1,000$

Please note that actual coupons are paid semi$-$annually, i$.$e$.,$ one half of the annual coupon.

Based on the information given above, please answer the following four questions:

$(1)$ What are the zero prices for the $6-$month, the $1-$year, the $18-$month, and the $2-$year Treasury securities above, respectively?

$(2)$ What is the $6-$month forward rate beginning $1$ year from today?

$(3)$ What is the $1-$year forward rate beginning $6$ months from today?

$(4)$ Given the zero prices obtained in $(1)$ above, what should be the price of a $2-$year T$-$note with $7\mathrm{.}5\%$ annual coupon $($also paid semi$-$annually$)$ with $$1,000$ par value per share?