$[$Related to Solved Problem $3\mathrm{.}1$B$]$ Some companies offer their employees defined benefit pension plans. Under these$$ plans, employees are promised a fixed monthly payment after they retire. An article on a financial planning website discussed the plans of some$$ companies, such as General Electric$($GE$),$ to offer some employees a$$ lump$-$sum, one$-$time payment if the employee would agree to not receive monthly pension payments.

The article$$ explains, "The amount of the lump sum is calculated by determining the present value of the$$ client's future$$ payments, using interest rate and life expectancy$$ assumptions."

Part $2$

Suppose that an employee expects to live to be $90$ years old and is entitled under$$ GE's retirement program to receive a pension of$$ $$1,000$ per month beginning at age $65.$

The total value of the payments the employee would receive over the $25$ years of payment would equal $$$enter your response here.

The lump sum amount GE will offer this employee would likely be

$$

greater than

less than

exactly equal to

the amount you found above since they will consider the

$$

discounted value of future payments

large benefit of receiving payments in the future

two payment options to be identical

$.$