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...

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Extracted 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.