Now it's time for you to practice what you've learned.

Suppose that Kate is $45$ years old and has no retirement savings. She wants to begin saving for retirement, with the first payment coming one year from now. She can save $$12,000$ per year and will invest that amount in the stock market, where it is expected to yield an average annual return of $15\mathrm{.}00\%$ return. Assume that this rate will be constant for the rest of her's life.

Kate would like to calculate how much money she will have at age $60.$

Using a financial calculator yields a future value of this ordinary annuity to be approximately $$570,964\mathrm{.}93$grad at age $60.$

Kate would now like to calculate how much money she will have at age $65.$

Using a financial calculator yields a future value of this ordinary annuity to be approximately at age $65.$

Kate expects to live for another $30$ years if she retires at age $60,$ with the same expected percent return on investments in the stock market.

Using a financial calculator, you can calculate that Kate can withdraw $$86,{958\mathrm{.}07}_{?}$ at the end of each year after retirement $($assuming retirement at age $60),$ assuming a fixed withdrawal each year and $$0$ remaining at the end of her life.

Kate expects to live for another $25$ years if she retires at age $65,$ with the same expected percent return on investments in the stock market.

Using a financial calculator, you can calculate that Kate can withdraw at the end of each year after retirement at age $65,$ assuming a fixed withdrawal each year and $$0$ remaining at the end of her life.