You look at your terminal to find some information about Treasury Notes and see the following:

Maturity $($years$)$ Face Value Zero Rate Coupon Price Yield

$1$ $$1001\%4\%--$

$2$ $$100.-6\%$ $$109.-$

$3$ $$1001\mathrm{.}50\%5\%$ $$110\mathrm{.}191\mathrm{.}42\%$

$4$ $$1001\mathrm{.}70\%3\%.--$

$5$ $$1001\mathrm{.}75\%.7\%.--$

Assume that all the notes pay only an annual coupon and continuously compounded.

that all the interest rates are

$1.($a$)$ What should the Futures price for delivery in $1$ year of an equity index that pays a continuously compounded dividend yield of $1\mathrm{.}5\%$ be$?$ The underlying index is trading at $$1000$ today. Assume forward prices and futures prices are the same.

$2.($b$)$ What is the price of the $1-$year Note?

$3.($c$)$ What is the yield of the $1-$year Note?

$4.($d$)$ Determine the zero$-$rate curve.

$5.($e$)$ What is the forward interest rate for the third year $($that is$,$ between T $=3$ and T $=4)?$

Assume this rate is $2\mathrm{.}5\%$ if you cannot find the solution to this question.

$6.($f$)$ What is today$$s value of a $$100,000$ FRA starting at year $3$ and lasting for one year with an agreed rate of $2\%?$ The cash$-$flow of this FRA is exchanged on year $3.$ Note that the FRA uses an annualized rate. Hint: you need to convert a continuously compounded rate to an annualized rate $($R $=$ er$\backslash$times $11).$

$7.($g$)$ What is the duration of the $3-$year Note?

$8.($h$)$ If the yield curve moves up by $5$bps$,$ what should the impact to the $3-$year Note be$?$

Does your answer still hold for a $2\%$ upward move? $3$