You will be paying $$20,000$ a year in maintenance expenses at the end of next

two years. Bond currently yield $7\%.$

$($a$)$ What are the present value and duration of your obligation?

$($b$)$ What maturity zero$-$coupon bond would immunize your obligation?

$7)$ A $30-$year maturity bond making annual coupon payments with a coupon

rate of $12\%$ has duration of $11\mathrm{.}54$ years and convexity of $187\mathrm{.}5.$ The bond currently

sells at a YTM of $8\%.$

a$)$ If the YTM falls to $7\%,$ what price would be predicted by the duration rule?

b$)$ What price would be predicted by the duration$-$with$-$convexity rule?

c$)$ Which method is more accurate? Support your answer.

$8.)$ Options give the right to buy or sell an underlying asset at a predetermined

price on or before the expiration date. Does this mean, all parties to the contract

enjoy no obligation? Support your answer.