Your pension plan will pay $$10,000$ once a year for a $10-$year period. The first payment will come in exactly five years. The current interest rate is $10\%$ per year. The duration of its obligation to you is $8\mathrm{.}7255$ years

$$ The pension fund wants to immunize its position. If the plan uses $5-$year and $20-$year zero$-$coupon bonds to construct the immunized position, how much money ought to be placed in each bond?