Pension funds pay lifetime annuities to recipients. If a firm remains 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 $16\%.$

Required:

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 eight 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 $5$ decimal places.$)$

b$.$ What will be the par value of your holdings in the $20-$year coupon bond? $($Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.$)$