$($i$)$ What is the approximate annualized yield on a $6-$month Treasury bill with a face value

of $$1000$ that is sold at $$970$ in the primary market? Show your workings in full $(2$

marks$)$

$($ii$)$ A $5-$year Treasury bond $($TBOND$1)$ is sold on the market one day at $$1000$ with an

annual coupon of $$60.$ The following day bad news hits the market and a new $5-$year

Treasury bond is sold on the market at an $$80$ annual coupon. What is the approximate

new secondary market price of TBOND$1?$ Show your workings in full $(3$ marks$)$

$($iii$)$ Write down an equation for the three main components of the nominal long term

interest rate on a bond, clearly explaining what each symbol stands for. $(2$ marks$)$

$($iv$)$ Draw a positively sloped yield curve and label it curve $1.$ On the same diagram draw

a new yield curve labelled curve $2$ if the expected rate of inflation both short and long

term falls. Label your axes carefully. $(3$ marks$)$