A $$10000$ bond with a coupon rate of $7\mathrm{.}6$

payable semiannually is redeemable after an unspecified number of years at $13500.$ The bond is bought to yield $9\%$ convertible semiannually. If the present value of the redemption value is $$3449\mathrm{.}28$ at this yield rate, find the purchase price.