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

Treasury

Security

Maturity Annual

Coupon

Price Par

Value

T$-$bill $6$ months $0\%$ $$984\mathrm{.}0240$ $$1,000$

T$-$bill $1$ year $0\%$ $$966\mathrm{.}1280$ $$1,000$

T$-$note $18$ months $3\mathrm{.}875\%$ $$999\mathrm{.}0625$ $$1,000$

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?