Your client is $34$ years old. She wants to begin saving for retirement, with the first payment to come one year from now. She can save $$13,000$ per year, and you advise her

to invest it in the stock market, which you expect to provide an average return of $10\%$ in the future.

a$.$ If she follows your advice, how much money will she have at $65?$ Do not round intermediate calculations. Round your answer to the nearest cent.

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b$.$ How much will she have at $70?$ Do not round intermediate calculations. Round your answer to the nearest cent.

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c$.$ She expects to live for $20$ years if she retires at $65$ and for $15$ years if she retires at $70.$ If her investments continue to earn the same rate, how much will she be able to

withdraw at the end of each year after retirement at each retirement age? Do not round intermediate calculations. Round your answers to the nearest cent.

Annual withdrawals if she retires at $65$:$

Annual withdrawals if she retires at $70$:$