Question 1 (a) Assume that a pension plan offers to pay $500,000 on a person's retirement (his/her sixty-fifth birthday) or a semi-annual annuity for the remainder of the person's life – i.e., starting 6 months from the date of retirement and including his/her date of death. Interest rates are 7 percent compounded annually, and a person's life expectancy has been determined statistically as being 78.5 years. Calculate the amount of the annuity that would make a person indifferent between the options? (b) A person joins a pension plan at age 40 (40th birthday). How much will s/he have to pay into the pension fund each year in order to accumulate a balance of $500,000 by the time s/he retires (age 65)? Assume that the final payment is on his/her 60th birthday. Interest rates are 9% compounded semi-annually.
Question 1 (a) Assume that a pension plan offers to pay $500,000 on a person's retirement (his/her sixty-fifth birthday) or a semi-annual annuity for the remainder of the person's life – i.e., starting 6 months from the date of retirement and including his/her date of death. Interest rates are 7 percent compounded annually, and a person's life expectancy has been determined statistically as being 78.5 years. Calculate the amount of the annuity that would make a person indifferent between the options? (b) A person joins a pension plan at age 40 (40th birthday). How much will s/he have to pay into the pension fund each year in order to accumulate a balance of $500,000 by the time s/he retires (age 65)? Assume that the final payment is on his/her 60th birthday. Interest rates are 9% compounded semi-annually.
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
Problem 1PS
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Transcribed Image Text:Question 1
(a) Assume that a pension plan offers to pay $500,000 on a person's retirement
(his/her sixty-fifth birthday) or a semi-annual annuity for the remainder of the
person's life – i.e., starting 6 months from the date of retirement and including
his/her date of death. Interest rates are 7 percent compounded annually, and a
person's life expectancy has been determined statistically as being 78.5 years.
Calculate the amount of the annuity that would make a person indifferent between
the options?
(b) A person joins a pension plan at age 40 (40th birthday). How much will s/he have
to pay into the pension fund each year in order to accumulate a balance of
$500,000 by the time s/he retires (age 65)? Assume that the final payment is on
his/her 60th birthday. Interest rates are 9% compounded semi-annually.
Transcribed Image Text:Question 2
(a) Laura Smith is planning for her and her husband Luke's retirement. Luke and
Laura, born on the same date, expect to retire in 30 years (when they both turn
65). The life expectancy of men is 78 years and the life expectancy of women is
87 years (i.e., assume that they die the day before their 78ith or 87th birthday).
During retirement (while they are living), the couple wants to withdraw $25,000, for
each of them, at the beginning of each year from their savings account. Assume
that the interest rate during their retirement is 12 percent compounded semi-
annually; the interest rate after Luke dies is 13 percent compounded annually; and,
the interest rate, prior to retirement, is 8 percent compounded annually. How
much will they have to deposit in their joint savings account (combine Luke and
Laura) each month (beginning one month from now and ending on their retirement
date)?
(b) Now assume that Luke and Laura Smith expect to inherit $25,000, 5 years from
now. If they save the money for their retirement, how much will they have to
deposit in their joint savings account (combine Luke and Laura) each month
(beginning one month from now and ending on their retirement date)?
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