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 $$3\mathrm{.}4$ million per year to beneficiaries. The yield to maturity on all bonds is $18\mathrm{.}5\%.$

Required:

a$.$ If the duration of $5-$year$-$maturity bonds with coupon rates of $14\mathrm{.}6\%($paid annually$)$ is four years and the duration of $20-$year$-$

maturity bonds with coupon rates of $8\%($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?

Note: Do not round intermediate calculations. Enter your answers in millions rounded to $2$ decimal places.

b$.$ What will be the par value of your holdings in the $20-$year coupon bond?

Note: Do not round intermediate calculations. Enter your answer in millions rounded to $2$ decimal places.