U$.$S$.$ Metallurgical Incorporated reported the following balances in its financial statements and disclosure notes at December $31,2023.$

Plan assets $ $570,000$

Projected benefit obligation $440,000$

U$.$S$.$M$.$s actuary determined that $2024$ service cost is $$77,000.$ Both the expected and actual rate of return on plan assets are $10\%.$ The interest $($discount$)$ rate is $5\%.$ U$.$S$.$M$.$ contributed $$137,000$ to the pension fund at the end of $2024,$ and retirees were paid $$61,000$ from plan assets.

Required:

What is the pension expense at the end of $2024?$

What is the projected benefit obligation at the end of $2024?$

What is the plan assets balance at the end of $2024?$

What is the net pension asset or net pension liability at the end of $2024?$

Prepare journal entries to record the $($a$)$ pension expense, $($b$)$ funding of plan assets, and $($c$)$ retiree benefit payments