A judge has ordered those meddling kids at Mystery, Inc. to pay $$5000$ one year from today and $$10000$ two years from today. To match the obligations, the Mystery, Inc. crew plans to purchase bonds today. The following bonds are available for purchase today:

$$ One$-$year zero$-$coupon bonds with $8\%$ yield

$$ Two$-$year $4\%$ par$-$value bond with annual coupons and $7\%$ yield

Find the total purchase price of the bonds today to exactly match the obligations: