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$ million per

year to beneficiaries. The yield to maturity on all bonds is $16\%.$

a$.$ If the duration of $5-$year maturity bonds with coupon rates of $12\%($paid annually$)$ is four years and the duration of $20-$year maturity

bonds with coupon rates of $6\%($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.$)$

b$.$ What will be the par value of your holdings in the $20-$year coupon bond? $($Do not round intermediate calculations. Enter your

answer in millions rounded to $2$ decimal places.$)$