$10.$ You have a single liability that requires a payment of $200,000$ at time $7.$ You want to create an immunized portfolio by buying two zero$-$coupon bonds that will mature in $4$ years and $10$ years respectively. The valuation interest rate for the liability and for both assets s$*$i$\_\{0\}=6\%.$ Find the amounts of the two bonds that you will buy, and verify that the portfolio is immunized.