# Your retirement plan: You hope to retire at age 62, and according to actuarial tables, you expect to live for 20 more years. You know of an investment option that will yield 4% annually compounded co…

Your retirement plan: You hope to retire at age 62, and according to actuarial tables, you expect to live for 20 more years. You know of an investment option that will yield 4% annually compounded continuously, and you plan to withdraw \$50,000 per year in retirement, for 20 years. How much money will you need to have in the account at the beginning of retirement so that you can withdraw \$50,000/year for 20 years? Begin your solution with letting R(t) represent the amount of money in the retirement account t years after you retire. For the "initial condition" assume that your retirement account runs out of money in 20 years (the initial condition is really a terminal condition here!). Write down the entire initial value problem -you may use technology to solve this. After getting the solution, determine R(0) to show how much money you will need to have at the beginning of retirement.