On January $1,2024,$ Splash City issues $$490,000$ of $8\%$ bonds, due in $15$ years, with interest payable semiannually on June $30$ and December $31$ each year. The market interest rate on the issue date is $9\%$ and the bonds issued at $$450,092.$

Required:

$1.$ Using an amortization schedule, show that the bonds have a carrying value of $$452,891$ on December $31,2025.($Round your final answers to nearest whole dollar.$)$