Products Ltd$.$ has a separate pension plan for its management. This pension plan was put in place on January$1,2013.$ The plan initiation created a pension obligation of $ $2$ million.$$ However, only $ $1\mathrm{.}5$ million was put into the plan initially. On January$1,2023,$ the company improved the benefits for the$$ plan, which increased the actuarial obligation by $ $700$ comma $000.$ The pension$$ plan's trustee and actuary provided the following information for the fiscal year ended December$31,2023$:

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Financial statements for the pension trust show$$ that, as at December$31,2022,$ plan assets were $ $4\mathrm{.}065$ million and the pension obligation was $ $5\mathrm{.}665$ million. The accounting$$ department's records indicate that $ $270$ comma $000$ was contributed into the pension fund during $2023.$ For purposes of interest$$ calculations, management assumes that all accruals and cash flows occur at the beginning of the fiscal year.

a$.$

Prepare the schedules showing the movements in the pension assets and liabilities during fiscal $2023.$

b$.$

Derive the pension expense for the fiscal year ended December$31,2023.$ Please show your work.

c$.$

Record the journal entries relating to the pension plan for the $2023$ fiscal year.