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Today is your aunt's $50$ th birthday. She expects to retire at age $70$ and actuarial tables suggest that your aunt will live to be $100.$ She wants to move to Hawaii when she retires $($at age $70)$ and estimates that the move will cost her $$200,000.$ She also estimates that her annual living

expenses in Hawaii will be $$25,000$ a year. She expects her savings will continue to earn an average rate of return of $7$ percent.

a$.$ How much will she need to have saved by her retirement date?

b$.$ She already has $$50,000$ in savings. How much would she need to save at the end of each of

the next twenty years to be able to afford this retirement plan?

c$.$ If she did not have any current savings and did not expect to be able to start saving money for the next five years $($that is$,$ her first savings will be made on her $55$th birthday$),$ how much would she have to set aside each year after that to be able to afford this retirement plan?