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 $1,2024.$ 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 $17$ yearsExpected life duration after retirement $23$ yearsTotal pension payment expected each year after retirement for all employees. Payment made at the endof the year. Amount includes all employees. $$417,000$ per yearThe interest rate to be used is $7\mathrm{.}50\%.$Required:Calculate the present value of this deferred annuity $($at January $1,2024).$