Question $1$

$($a$)$ A three$-$year $$1000$ bond has a $6$ percent coupon rate. If the current market price is

$$900.$

$($i$)$ Estimate the yield to maturity

$($ii$)$ If interest rates suddenly drop to $3$ percent per annum on similar three$-$year

bonds, how would investors in the bond market react to this bond and what

happens to its price?

$($b$)$ If the interest rate is $10\%$ per annum.

$($i$)$ What is the present value of a security that pays $$1100$ next year, $$1200$ the

year after that, and $$1400$ the year after that?

$($ii$)$ If the asset in part $($i$)$ is sold for $$3000,$ is the yield to maturity more or less

than $10\%?$xplain.