Suppose that Ana is $40$ 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 $$30,000$ per year and will invest that amount in the stock market, where it is expected to yield an average annual return of $10\mathrm{.}00\%$ return. Assume that this rate will be constant for the rest of her$$s life. In short, this scenario fits all the criteria of an ordinary annuity.

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

Use the following table to indicate which values you should enter on your financial calculator. For example, if you are using the value of $1$ for N$,$ use the selection list above N in the table to select that value.

Input $2010\mathrm{.}00\%0-$$$30,000$

Keystroke N I$/$Y PV PMT FV

Output $?$

Using a financial calculator yields a future value of this ordinary annuity to be approximately $$1,718,249\mathrm{.}98$ at age $60.$

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

Use the following table to indicate which values you should enter on your financial calculator. For example, if you are using the value of $1$ for N$,$ use the selection list above N in the table to select that value.

Input $2510\mathrm{.}00\%0-$$$30,000$

Keystroke N I$/$Y PV PMT FV

Output $?$

Using a financial calculator yields a future value of this ordinary annuity to be approximately $$2,950,411\mathrm{.}78$ at age $65.$

Ana 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.

She would like to calculate how much she can withdraw at the end of each year after retirement.

Use the following table to indicate which values you should enter on your financial calculator in order to solve for PMT in this scenario. For example, if you are using the value of $1$ for N$,$ use the selection list above N in the table to select that value.

Input Amount saved for retirement by age $600$

Keystroke N I$/$Y PV PMT FV

Output $?$

Using a financial calculator, you can calculate that Ana can withdraw 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.

Ana 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.

Use the following table to indicate which values you should enter on your financial calculator. For example, if you are using the value of $1$ for N$,$ use the selection list above N in the table to select that value.

Input Amount saved for retirement by age $650$

Keystroke N I$/$Y PV PMT FV

Output $?$

Using a financial calculator, you can calculate that Ana 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.