Rocky and Bullwinkle are obligated to make a payment of $$10000$ in $8$ years. To provide for this obligation, they make the following purchases:

$$ An $6-$year zero$-$coupon bond purchased for $ A$.$

$$ An $11-$year zero$-$coupon bond purchased for $ B$.$

$($a$)$ Find the purchase prices A and B such that the zero$-$coupon bonds and the debt obligation form a portfolio which satisifies the conditions for Redington immunization at an effective annual interest rate of $3\mathrm{.}5\%.$ Round your answers to the nearest cent.$=$ $

$=$ $

$($b$)$ Using your answers from $($a$),$ find the difference in the Macaulay convexities of Rocky and Bullwinkle's assets and liabilities at an annual interest rate of $3\mathrm{.}5\%.$ In other words, verify the third condition for Redington immunization holds for your values of A and B$.$ Round your answer to three decimal places.

$(0\mathrm{.}035,\backslash$infty $).(0\mathrm{.}035,\backslash$infty $)$ years