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(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 Sx 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? (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?

(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 Sx 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? (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?

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
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(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? (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?
Transcribed Image Text:(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? (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?
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