The current on$-$the$-$run yields for the Ramsey Corporation are as follows:

Assume that each bond is an annual$-$pay bond. Each bond is trading at par, so its coupon rate is equal to its yield

to maturity.

Answer the below questions.

$($a$)$ Using the bootstrapping methodology, complete the following table:

$($b$)$ Using the spot rates, what would be the value of an $8\mathrm{.}5\%$ option$-$free bond of this issuer?

$($c$)$ Using the one$-$year forward rates, what would be the value of an $8\mathrm{.}5\%$ coupon option$-$free bond of this issuer?

$($d$)$ Using the binomial model $($which assumes that one$-$year rates undergo a lognormal random walk with volatility

$),$ show that if $$ is assumed to be $10\%,$ the lower one$-$year forward rate one year from now cannot be $7\%.$

$($e$)$ Demonstrate that if $$ is assumed to be $10\%,$ the lower one$-$year forward rate one year from now is $6\mathrm{.}944\%.$

$($f$)$ Demonstrate that if $$ is assumed to be $10\%,$ the lower one$-$year forward rate two years from now is

approximately $6\mathrm{.}437\%.$

$($g$)$ Show the binomial interest$-$rate tree that should be used to value any bond of this issuer.

$($h$)$ Determine the value of an $8\mathrm{.}5\%$ coupon option$-$free bond for this issuer using the binomial interest$-$rate tree given

in part $g.$

$($i$)$ Determine the value of an $8\mathrm{.}5\%$ coupon bond that is callable at par $(100)$ assuming that the issue will be called

if the price exceeds par.