Modified from P$17-2)$ Buckeyes defined benefit pension plan specifies annual retirement benefits equal to: $3\mathrm{.}0\%$ service years $$ final year$$s salary, payable at the end of each year. James was hired by Buckeyes at the beginning of $2004$ and is expected to retire at the end of $2033$ after $30$ years$$ service. His retirement is expected to span $20$ years. James$$ salary is projected to be $$250,000$ at retirement. The actuary$$s discount rate is $6\%.$

Present value of $$1$: n $=10,$ i $=6\%$ is $0\mathrm{.}55839.$

Present value of $$1$: n $=15,$ i $=6\%$ is $0\mathrm{.}41727$

Present value of $$1$: n $=20,$ i $=6\%$ is $0\mathrm{.}31180$

Present value of $$1$: n $=30,$ i $=6\%$ is $0\mathrm{.}17411$

Present value of an ordinary annuity: n $=10,$ i $=6\%$ is $7\mathrm{.}36009$

Present value of an ordinary annuity: n $=15,$ i $=6\%$ is $9\mathrm{.}71225$

Present value of an ordinary annuity: n $=20,$ i $=6\%$ is $11\mathrm{.}46992$

Present value of an ordinary annuity: n $=30,$ i $=6\%$ is $13\mathrm{.}76483$

$$

Required:

Estimate by the projected benefit approach the portion of James$$ annual retirement payment earned as of the end of $2018.(3$ points$)$

What is the company$$s PBO at the end of $2018$ with respect to James. $(5$ points$)$

If no estimates are changed in the meantime, what will be the company$$s PBO at the end of $2023?(6$ points$)$