Emily Jacob is 45 years old and has saved nothing for retirement. Fortunately, she just inherited $76,000. Emily plans to put a large portion of that money into an investment account earning a(n) 12% return. She will let the money accumulate for 20 years, when she will be ready to retire. She would like to deposit enough money today so she could begin making withdrawals of $41,000 per year starting at age 66 (21 years from now) and continuing for 24 additional years, when she will make her last withdrawal at age 90. Whatever remains from her inheritance, Emily will spend on a shopping spree. Emily will continue to earn 12% on money in her investment account during her retirement years, and she wants the balance of her retirement account to be $0 after her withdrawal on her ninetieth birthday.

a. How much money must Emily set aside now to achieve that goal? It may be helpful to construct a timeline to visualize the details of this problem.

b. Emily realizes that once she retires she will want to have less risky investments that will earn a slightly lower rate of return, 7% rather than 12%. If Emily can earn 12% on her investments from now until age 65, but she earns just 7% on her investments from age 65 to 90, how much money does she need to set aside today to achieve her goal?

c. Suppose Emily puts all of the $76,000 that she inherited into the account earning 12%. As in part b, she will earn only a(n) 7% return on her investments after age 65. If Emily withdraws $41,000 as planned on each birthday from age 65 to age 90, how much will be left in her account for her heirs after her last withdrawal?