An insurance company must make payments to a customer of $$10$ million in one year and $$4$ million in five years. The yield curve is flat

at $10\%.$

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? $($Do not round intermediate calculations. Round your answer to $4$ decimal places.$)$

Maturity of zero coupon bond

years

b$.$ What must be the face value and market value of that zero$-$coupon bond? $($Do not round intermediate calculations. Enter your

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