Funding your retirement Emily Jacob is $45$ years old and has saved nothing for retirement. Fortunately, she just nherited $$80,000.$ Emily plans to put a large portion of that money into an investment account earning a$($n$)15\%$ return. She will let the money accumulate for $20$ years, when she will be ready to retire. She would like to deposit enough money today so she could begin making withdrawals of $$49,000$ 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 $15\%$ 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 $15\%.$ If Emily can earn $15\%$ 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 $$80,000$ that she inherited into the account earning $15\%.$ As in part $b,$ she will earn

a$.$ The amount Emily must set aside now is $ $($Round to the nearest cent.$)$

b$.$ The amount Emily needs to set aside to achieve her goal is $ $($Round to the nearest cent.$)$

c$.$ The amount that will be left in the account for her heirs is $ $($Round to the nearest cent.$)$