A $5\%$ coupon bond has a par value of $$1,000$ and $13$ years remaining until maturity. Coupons are paid semi$-$annually. If the bond's yield$-$to$-$maturity is $5\mathrm{.}4\%,$ what is its price? Enter your answer as a positive number rounded to the nearest penny.

NOTE: Once you have correctly answered this question, you can start with the YTM you found, use the same values for par, coupon, and years to maturity as above, and solve for the bond's price.