You're 30 years old. By some miracle of maturity, you've man- aged to save $100,000 for retirement in an IRA. You estimate that the funds in this IRA will earn 6% per year, compounded monthly, for the next 30 years. You want to retire in exactly 30 years at age 60, and you've determined that you can afford to put $X per month into the account starting next month and then continuing for the subsequent 359 months straight until you retire. When you retire, you plan to use the entire balance in your IRA to purchase an ordinary annuity that pays monthly payments of $4,000 for your expected remaining life of 1:
You're 30 years old. By some miracle of maturity, you've man- aged to save $100,000 for retirement in an IRA. You estimate that the funds in this IRA will earn 6% per year, compounded monthly, for the next 30 years. You want to retire in exactly 30 years at age 60, and you've determined that you can afford to put $X per month into the account starting next month and then continuing for the subsequent 359 months straight until you retire. When you retire, you plan to use the entire balance in your IRA to purchase an ordinary annuity that pays monthly payments of $4,000 for your expected remaining life of 1:
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:You're 30 years old. By some miracle of maturity, you've man-
aged to save $100,000 for retirement in an IRA. You estimate that the
funds in this IRA will earn 6% per year, compounded monthly, for
the next 30 years. You want to retire in exactly 30 years at age 60, and
you've determined that you can afford to put $X per month into the
account starting next month and then continuing for the subsequent
359 months straight until you retire. When you retire, you plan to use
the entire balance in your IRA to purchase an ordinary annuity that
pays monthly payments of $4,00o for your expected remaining life of
40 years. This annuity is priced so that its discount rate is 3% (com-
pounded monthly). We ignore inflation throughout this problem.
Find X, the amount you need to start investing on a monthly basis to
reach your retirement goal.
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