Assume that Matthew Young, age $30,$ begins employment with Crane Corp. on January $1,2022,$ at a starting salary of $$38,010.$ It is

expected that Matthew will work for Crane for $35$ years, retiring on December $31,2056,$ when Matthew is $65$ years old. If we estimate

that Matthew's salary will increase approximately $4\%,$ Matthew's salary at retirement is expected to be $$150,000.$ Assume that

mortality tables indicate the life expectancy of someone aged $65$ in $2056$ is $12$ years. The company has the following pension benefit

formula: Annual pension benefit on retirement $=2\%$ final salary $$ years of service. A discount rate of $6\%$ is assumed to be the current

yield on high$-$quality debt instruments.

Assume it is now $2024,$ three years after the defined benefit pension plan for Matthew Young was initiated. In December $2024,$

Crane's actuary provided the company with an actuarial revaluation of the plan. The actuary's assumptions included the following

changes:

Estimated final salary on retirement $$154,000$

Current settlement$/$discount rate $7\%$

Click here to view the factor table.$($a$)$

Calculate the defined benefit obligation at December $31,2024,$ and the amount of any actuarial gain or loss. Use a financial

calculator of Excel functions for your calculation of the $7\%$ rate. $($For calculation purposes, use $5$ decimal places as displayed in the

factor table provided and round answers to $0$ decimal places, e$.$g$.5,275.)$

DBO at Dec. $31,2024$