$Q2.[20$ Marks$]$

$(a)[15$ Marks$]$ A fixed interest security $of$ nominal amount $1,000,000istobe$ issued. This security

pays coupons monthly $in$ arrears $at$ a rate $of9\%$ per annum. The security $istobe$ redeemed with $a$

capital payment $of120$ per $100$ nominal $on$ a coupon date between $15$ and $20$ years, inclusive,

after the date $of$ issue. The redemption date $isat$ the option $of$ the borrower.

$An$ investor, who $is$ liable $to$ income tax $at30\%$ payable $at$ the same time $as$ the coupons are paid

and capital gains tax $of43\%$ payable $3$ months after redemption, wishes $to$ purchase the entire

security $at$ the date $of$ issue, $at$ a price that ensures that the investor achieves a net effective yield

$ofat$ least $6\%$ per annum.

$(i)[10$ Marks$]$ Calculate the maximum price that the investor should pay per $100$

$(ii)[2$ marks$]If$ the coupons had been payable more frequently than monthly, would that increase

$or$ decrease the maximum price $tobe$ paid $by$ the investor? Justify your answer.

$(iii)[3$ Marks$]If$ redemption $isat$ par, what effect $if$ any, $it$ will have $on$ calculating the price $in$

part $(i)?$ Justify your answer.

$(b)[5$ Marks$]$ Suppose that the force $of$ interest spot rate per annum $is$ given $by$

$Yt=0\mathrm{.}6-0\mathrm{.}02t$

Calculate the instantaneous forward rate per annum $at$ time $15$ years, $i.e.$ calculate $F15no$ chatgpt $no$ excel $on$ paper please