Liability payments of $100$ each are due to be paid in $2,4$ and $6$ years from now. Asset cashflow consists of $A_1$ in $1$ year and $A_5$ in $5$ years. The yield for all payments is $10\%.$ An attempt is made to have the asset cash flow immunize the liability cashflow by matching present value and duration.

$($a$)$ Find $A_1$ and $A_5.$

$($b$)$ Determine whether or not the conditions for Redington immunization are satisfied.