You own a $$1000$ face value $5-$year bond with semiannual coupons that will mature is $3$ years. Immediately after receiving the $4^{th}$ coupon of $$45,$ you sell the bond and purchase another newly issued $$1000$ face value $5-$year bond with semiannual coupons of $$50$ each. Given that the prevailing market rate is $r^{(2)}=8\%$ and the bond you originally owned is redeemable at $105\%,$ find the redemption value of the new bond that you purchase.