An insurance company must make a payment of $$30,000$ in $10$ years. The market interest rate is $6\%.$ The company's portfolio manager wishes to fund the obligation using $5-$year zero$-$coupon bonds and perpetuities paying $$500$ annual coupons. To immunize the obligation, what is the asset weight for the zero$-$coupon bonds and how much of zero$-$coupon bonds you want to hold?

$60\mathrm{.}53\%,$$$10,139\mathrm{.}27$

$57\mathrm{.}65\%,$$$9657\mathrm{.}44$

$39\mathrm{.}12\%,$$$6\mathrm{.}456\mathrm{.}58$

$64\mathrm{.}35\%,$$$10779\mathrm{.}81$