$5.$ You are the CFO of the firm Ponce deLeon Foods. The board has decided to offer an early retirement plan whereby the typical $55-$year$-$old worker can retire now with a small cash severance and draw a pension of $$10,000$ a year, expected to last for $30$ years $($the first payment would be made one year from now$).$ You plan to set aside sufficient money now to fund the plan and have secured guarantees from your insurance company promising you an $8\%$ annual return on all funds deposited by you, to meet these projected payments based on the terms above, and to bear any risk $($such as interest$-$rate surprises or greater$-$than$-$expectedlifespans$).$ You expect $100$ workers to take advantage of the plan, so you must fund expected pension payouts of $$1$ million a year for $30$ years.The Amalgamated Paper$-$or$-$Plastic Workers have objected to the plan, since the pension payments "lose purchasing power" over time due to inflation. They propose an alternative plan of an $$8,000$ pension $($also beginning in a year$)$ that grows each year at a fixed rate of $5\%.$ They claim that this plan should be attractive to the company, since it needs to pay less money to pensioners $($$$8,000$ vs$.$ $$10,000$ during today's difficult economic times.How much will it cost you for an up$-$front payment to fund each plan?HINT: While vou could easily solve this on a spreadsheet. you may instead choose to use the formula below for the present value $($V$)$ of an initial end$-$of$-$vear annuity pavout of SC $($growing at q$\%)$ per period, with an interest rate of r$\%.$ for T periods