Pension funds pay lifetime annuities to recipients. If a firm will remain in business indefinitely, the pension obligation will resemble a perpetuity. Suppose, therefore, that you are managing a pension fund with obligations to make perpetual payments of $$2\mathrm{.}6$ million per year to beneficiaries. The yield to maturity on all bonds is $11\mathrm{.}5\%.$

a$.$ If the duration of $5-$year maturity bonds with coupon rates of $12\mathrm{.}6\%($paid annually$)$ is four years and the duration of $20-$year maturity bonds with coupon rates of $4\%($paid annually$)$ is $11$ years, how much of each of these coupon bonds $($in market value$)$ will you want to hold to both fully fund and immunize your obligation? $($Do not round intermediate calculations. Enter your answers in millions rounded to $1$ decimal place.$)$

$\backslash$table$[[,,],[5-$year bond,,million$],[20-$year bond,,million$]]$

b$.$ What will be the par value of your holdings inthe $20-$year coupon bond? $($Do not round intermediate calculations. Enter your answer in millions rounded to $2$ decimal places.$)$

Par value

million