Suppose that you start working for a company at age $25.$ You are offered two rather unlikely, but quite enticing, retirement plans from which you are allowed to choose one. $[$Round all answers to the nearest dollar.$]$

Retirement plan $1$: When you retire, you will receive $$16,000$ for each year of service.

Retirement plan $2$: When you start work, the company deposits $$2500$ into a savings account that is guaranteed to pay a yearly rate of $17\%.$ When you retire, the account will be closed and the balance given to you.

A$.$ Determine the amount you would receive under plan $1,$ if you retiked at age $55$

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B$.$ Determine the amount you would receive under plan $1,$ if you retired at age $65.$

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C$.$ Determine the amount you would receive under plan $2,$ if you retired at age $55.$

D$.$ Determine the amount you would receive under plan $2,$ if you retired at age $65.$

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