Problem $16-9($Algo$)$

An insurance company must make payments to a customer of $$12$ million in one year and $$7$ million in four years. The yield curve is flat at $5\%.$

Required:

a$.$ If it wants to fully fund and immunize its obligation to this customer with a single issue of a zero$-$coupon bond, what maturity bond must it purchase?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

b$.$ What must be the face value and market value of that zero$-$coupon bond?

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

$\backslash$table$[[$a Maturity of zero coupon bond,years$],[$b$.$ Face value,million$],[$b$.$ Market value,million$]]$