$(6$ points$)$ Nerwin, Inc. is a furniture manufacturing company with $50$ employees.

Recently, after a long negotiation with the local labor union, the company decided to

initiate a pension plan as a part of its compensation plan. The plan will start on January $1,$

Each employee covered by the plan is entitled to a pension payment each year after

retirement. On the basis of a discussion with the supervisor of the Personnel Department

and an actuary from an insurance company, the controller develops the following

information related to the pension plan.

Average length of time to retirement

Expected life duration after retirement

Total pension payment expected each year after

retirement for all employees. Payment made at the end

of the vear. Amount includes all emblovees.

$17$ years

$23$ years

$$417,000$ per

year

The interest rate to be used is $7\mathrm{.}50\%.$

Required:

Calculate the present value of this deferred annuity $($at January $1,2024).$