1. A retirement annuity of 30 annual payments (each payment is $50,000) begins 20 years from today. The value of that annuity 20 years from today is __________________. The value of that annuity 19 years from today is ___________________. The value of that annuity today is ___________________. if the problem does not specify an interest rate, assume the rate to be 12%

2. (a) Assume that a pension plan offers to pay a lump sum of $200,000 on a person's 65th birthday, or an annuity of $x for the remainder of the person's life. Interest rates are 10 percent, and a person's life expectancy has been determined statistically as being 80 years. What is the value of x (the amount of the annuity) that would make the two alternatives equivalent on an expected present value basis? if the problem does not specify an interest rate, assume the rate to be 12%

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(b) A person joins the pension plan at age 30. How much will she have to pay into the pension fund at the end of each year in order to accumulate a balance of $150,000 in the fund at age 65? if the problem does not specify an interest rate, assume the rate to be 12%